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PERFORMANCE ANALYSIS AND SIMULATION OF
AN AUTONOMOUS UNDERWATER VEHICLE EQUIPPED
WITH THE COLLECTIVE AND CYCLIC PITCH PROPELLER
By
MINH QUANG TRAN, B.Eng (Aerospace Engineering)
National Centre for Maritime Engineering and Hydrodynamics
Australian Maritime College
College of Sciences and Engineering
Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy
University of Tasmania
December 2017
To my family, my love, and my PhD supervisors.
Declaration of Originality
This thesis contains no material which has been accepted for a degree or diploma by the Uni-
versity or any other institution, except by way of background information and duly acknowl-
edged in the thesis, and to the best of my knowledge and belief no material previously pub-
lished or written by another person except where due acknowledgement is made in the text
of the thesis, nor does the thesis contain any material that infringes copyright.
Minh Quang Tran
December 2017
Statement of Authority of Access
This thesis may be made available for loan and limited copying in accordance with the Copy-
right Act 1968.
Minh Quang Tran
December 2017
Statement of Co-Authorship
The following people and institutions contributed to the publication of work undertaken as
part of this thesis:
Minh Quang Tran, University of Tasmania (Candidate)
Dr Hung Nguyen, University of Tasmania (Author 1)
Associate Professor Jonathan Binns, University of Tasmania (Author 2)
Associate Professor Shuhong Chai, University of Tasmania (Author 3)
Assistant Professor Alexander Forrest, University of California Davis (Author 4)
Authors details and their roles:
Conference Papers
Paper 1 (Part of Chapter 1). A Study of new propulsion system for an Autonomous Underwa-
ter Vehicle, 9th Graduate Research Conference at the University of Tasmania, Hobart, Australia, 2015.
Candidate was the primary author and with author 1, author 2, author 3, and author 4 con-
tributed to the ideas and presentation.
Paper 2 (Part of Chapter 6). Performance Prediction of Autonomous Underwater Vehicle with
Different Propulsion System Configurations. International Conference on Modelling and Simula-
tion for Autonomous Systems. Springer, 72-82.
Candidate was the primary author and with author 1, author 2, author 3, and author 4 con-
tributed to the ideas and refinement.
Paper 3 (Part of Chapter 7). Least Squares Optimisation Algorithm Based System Identification
of an Autonomous Underwater Vehicle, Proceedings of the 3rd Vietnam Conference on Control and
Automation, Vietnam, 2015.
Candidate was the primary author and with author 1 contributed to the control algorithm.
Author 2, author 3, and author 4 contributed to the ideas and refinement.
Paper 4 (Part of Chapter 7). Optimal control of an autonomous underwater vehicle equipped
with the collective and cyclic pitch propeller. Control Conference (ASCC), 2017 11th Asian. IEEE,
354-359.
Candidate was the primary author and with author 1 contributed to the refinement and
presentation. Author 2, author 3, and author 4 contributed to the ideas and refinement.
Journal Papers
Paper 5 (Part of Chapter 4). A practical approach to the dynamics modelling of an underwater
vehicle propeller in all four quadrants of operation, Proceedings of the Institution of Mechanical
Engineers, Part M: Journal of Engineering for the Maritime Environment. (Published).
Candidate was the primary author with the laboratory assistance from author 1 and author 2.
Author 3 and author 4 contributed to the ideas and refinement.
Paper 6 (Part of Chapter 5). Experimental Study of the Collective and Cyclic Pitch Propeller,
The Journal of Marine Science and Application. (Accepted for publication).
Candidate was the primary author with the laboratory assistance from author 1 and author 2.
Author 3 and author 4 contributed to the ideas and refinement.
Paper 7. A comparison study of two propulsion system configurations for an autonomous
underwater vehicle, Ocean Engineering, An International Journal of Research and Development. (In
progress).
Candidate was the primary author and with author 1, author 2, author 3, and author 4 con-
tributed to the ideas and refinement.
We the undersigned agree with the above stated “proportion of work undertaken” for each of
the above published (or submitted) peer-reviewed manuscripts contributing to this thesis:
Signed:
………………………..............
Primary Supervisor
Australian Maritime College
University of Tasmania
………………………………..
Head of School
Australian Maritime College
University of Tasmania
i
ABSTRACT
There is a growing need within marine sciences and engineering that requires the torpedo
shaped Autonomous Underwater Vehicles (AUVs) being capable of accomplishing various
complex surveillance missions, including scientific, commercial and military applications. Be-
sides the traditional research on the control and navigation of an AUV, the propulsion system
study becomes more and more essential to increase the manoeuvrability and efficiency of AUV.
The conventional propulsion system with fixed pitch propeller (FPP) and control surfaces at
the aft end is the predominant propulsion type used by AUVs. This propulsion configuration
has the shortcoming of insufficient low-speed manoeuvrability since the control surface
manoeuvring forces are only generated when the vehicle is in motion. This is one of the fun-
damental limiting factors for the current torpedo shaped AUVs. The development of new pro-
pulsion system enabling both low speed and cruising speed operations could expand the typ-
ical operational envelope of an underwater vehicle and pave the way for the new applications.
This thesis focuses on the characteristic analysis of an innovative propulsion system called the
Collective and Cyclic Pitch Propeller (CCPP) and the manoeuvring performance of an AUV
equipped with CCPP. In the CCPP mechanism, the angles of each propeller blade can be po-
sitioned periodically during a rotation in both collective and cyclic pitch setting. CCPP has the
capability to provide continuous propulsive force and manoeuvring forces simultaneously.
The primary task of the thesis was to explore the feasibility of a prototype CCPP to an under-
water vehicle by numerically conducting the comparison between the AUV equipped with
CCPP and FPP in standard manoeuvring tests. Initially, the Experimental Fluid Mechanics
ii
approach was utilised to investigate the performance and derive the mathematical models of
the CCPP and FPP. Two separate experimental apparatus were designed and implemented in
this research for CCPP and FPP system. In the first experiment, the dynamic modelling of FPP
using the four-quadrant model was proposed based on experimental data. The second exper-
imental study involved the extensive investigation of the CCPP to establish its hydrodynamic
characteristics. A series of comprehensive bollard pull and captive model tests were designed
and conducted to evaluate the propulsion performance. Furthermore, the research developed
a numerical simulation program called AUVSIPRO to examine the performance and manoeu-
vring characteristics of an AUV equipped with the CCPP as well as conventional configuration
FPP. The Gavia AUV was used as the research platform and its mathematical model with non-
linear hydrodynamic coefficients were defined using the theoretical approach. Standard
manoeuvring tests of marine vehicles were fully presented in the simulation program to ana-
lyse the manoeuvrability. In addition, the results from the experiments and simulation were
utilised in the comparison study between the CCPP and conventional configuration applied
to AUV. Finally, the controller design for an AUV equipped with a CCPP was conducted. The
two-stage system identification method was proposed to develop the linear system model,
which was applicable for the control design. The optimal state feedback algorithm was pre-
sented as the control strategy.
The propulsion systems for AUV have been subject to an increased focus with respect perfor-
mance and manoeuvrability. This research is an exploration into the feasibility and viability
of CCPP propulsion system for a torpedo shaped AUV and contributes to the areas related to
the development of propulsion system for an underwater vehicle.
iii
ACKNOWLEDGEMENTS
I would like to express my special appreciation and thanks to my primary supervisor, Dr.
Hung Duc Nguyen, for his relentless support and encouragement during the past three years.
I also would like to acknowledge my co-supervisors, Associate Professor Jonathan Binns, As-
sociate Professor Shuhong Chai at the Australian Maritime College, University of Tasmania;
and Assistant Professor Alexander Forrest at the University of California Davis, who provided
me with their supportive and valuable guidance throughout the course of my research project.
I am grateful to the members of the technician team at the Australian Maritime College, Uni-
versity of Tasmania for their assistance on the accomplishment of the experiments in the Tow-
ing Tank.
I also would like to thank the University of Tasmania for the financial support from the Tas-
mania Graduate Research Scholarship.
My deepest appreciation is to my parents, my family, my love and all of my friends for their
endless dedication and encouragement.
Minh Quang Tran
Tasmania, Australia
December 2017
iv
“Shoot for the moon. Even if you miss it you will land among the stars.”
v
TABLE OF CONTENTS
ABSTRACT ........................................................................................................................................... i
ACKNOWLEDGEMENTS .............................................................................................................. iii
TABLE OF CONTENTS ..................................................................................................................... v
LIST OF FIGURES ............................................................................................................................. xi
LIST OF TABLES .............................................................................................................................xvi
NOMENCLATURE ........................................................................................................................ xvii
ABBREVIATIONS ........................................................................................................................... xxi
CHAPTER 1 ......................................................................................................................................... 1
Introduction ......................................................................................................................................... 1
1.1 Motivation .................................................................................................................. 2
1.2 Scope of the Thesis .................................................................................................... 7
1.3 Contribution to Research .......................................................................................... 9
1.4 Outline of the Thesis ................................................................................................. 9
1.5 Publications .............................................................................................................. 11
1.5.1 Presentations and Conference Papers ................................................................... 11
1.5.2 Journal Papers .......................................................................................................... 11
CHAPTER 2........................................................................................................................................ 13
Literature Review ............................................................................................................................. 13
vi
2.1 Introduction.............................................................................................................. 14
2.2 Conventional propulsion system for an autonomous underwater vehicle and
its limitations ........................................................................................................................ 14
2.2.1 Conventional propulsion system with Fixed Pitch Propeller (FPP) ................. 14
2.2.2 Limitations of the conventional propulsion system ........................................... 15
2.3 Alternative Propulsion Systems for an Underwater Vehicle ............................. 16
2.3.1 Thruster ..................................................................................................................... 16
2.3.2 Vectored Thruster .................................................................................................... 17
2.3.3 Buoyancy Engine ..................................................................................................... 18
2.3.4 Biomimetic propulsion ........................................................................................... 19
2.3.5 Preswirl Propulsor................................................................................................... 20
2.3.6 Jet-pump or waterjet Propulsion ........................................................................... 21
2.3.7 Hybrid Propulsors ................................................................................................... 22
2.4 Collective and Cyclic Pitch Propeller (CCPP)...................................................... 22
2.5 Summary .................................................................................................................. 27
CHAPTER 3 ....................................................................................................................................... 28
AUV Equations of Motion .............................................................................................................. 28
3.1 Introduction.............................................................................................................. 29
3.2 Coordinate Systems and Transformation ............................................................ 30
3.2.1 Six Degree of Freedom and Standard Notation .................................................. 30
3.2.2 Coordinate Systems ................................................................................................. 31
3.2.3 Euler Angles and Vector Transformation ............................................................. 32
vii
3.3 Kinematics ................................................................................................................ 33
3.4 Dynamics .................................................................................................................. 34
3.4.1 Equations of Motion for Underwater Vehicle ...................................................... 34
3.4.2 External Rigid Body Force ...................................................................................... 36
3.4.3 Determination of the Hydrodynamic Coefficients ............................................. 41
3.5 Summary .................................................................................................................. 45
CHAPTER 4 ....................................................................................................................................... 46
Experimental Study of the Conventional Fixed Pitch Propeller .............................................. 46
4.1 Introduction.............................................................................................................. 48
4.2 Propeller Dynamic Modelling ............................................................................... 50
4.2.1 The Propeller Open Water Characteristics Curves ............................................. 50
4.2.2 The Propeller Four-quadrant Mathematical Model ............................................ 52
4.2.3 Four-quadrant Model Representations ................................................................ 53
4.2.4 The Least Squares Fitting Method ......................................................................... 55
4.3 Experimental Study ................................................................................................. 56
4.3.1 Open Water Test Setup............................................................................................ 57
4.3.2 Data Acquisition and Post Processing .................................................................. 59
4.3 Results and Discussions.......................................................................................... 61
4.3.1 Open Water Performance Results .......................................................................... 61
4.3.1 Four-quadrant Models Results .............................................................................. 62
4.4 Summary .................................................................................................................. 70
viii
CHAPTER 5 ....................................................................................................................................... 71
Experimental Study of the Collective and Cyclic Pitch Propeller CCPP ................................ 71
5.1 Introduction.............................................................................................................. 72
5.2 Experimental Design ............................................................................................... 73
5.2.1 Experimental setup ................................................................................................. 73
5.2.2 Force and moment measurements ........................................................................ 74
5.2.3 Data acquisition system and signal conditioning ............................................... 76
5.2.4 Experimental program ............................................................................................ 76
5.2.5 Data reduction and representation ....................................................................... 77
5.2.6 Error analysis ........................................................................................................... 78
5.2 Results and Discussions.......................................................................................... 79
5.2.1 Bollard pull test ........................................................................................................ 79
5.2.2 Captive model test ................................................................................................... 85
5.3 Summary .................................................................................................................. 89
CHAPTER 6 ....................................................................................................................................... 90
Manoeuvring Simulation ................................................................................................................ 90
6.1 Introduction.............................................................................................................. 92
6.2 AUVSIPRO – The Simulation Program Description .......................................... 92
6.3 Manoeuvring Design .............................................................................................. 97
6.3.1 Acceleration Manoeuvre Test ................................................................................ 97
6.3.2 Stopping Test ............................................................................................................ 98
6.3.3 Turning Circle Manoeuvre ..................................................................................... 99
ix
6.3.4 Static Turning Manoeuvre .................................................................................... 100
6.3.5 Pull-out Manoeuvre .............................................................................................. 100
6.3.6 Zig-Zag Manoeuvre .............................................................................................. 100
6.3.7 Depth-changing manoeuvre ................................................................................ 101
6.3.8 Meander Manoeuvre ............................................................................................. 102
6.3.9 Spiral Manoeuvre or Helix Manoeuvre .............................................................. 103
6.3.10 Reverse Spiral .................................................................................................... 104
6.4 Results and Discussion ......................................................................................... 104
6.4.1 Acceleration Manoeuvre Test .............................................................................. 104
6.4.2 Stopping Manoeuvre Test .................................................................................... 109
6.4.3 Static Turning Manoeuvre .................................................................................... 113
6.4.4 Zigzag Manoeuvre ................................................................................................ 116
6.4.5 Depth-Changing Manoeuvre ............................................................................... 118
6.5 Summary ................................................................................................................ 120
CHAPTER 7 ..................................................................................................................................... 122
CONTROL APPLICATION .......................................................................................................... 122
7.1 System Identification ............................................................................................. 125
7.1.1 Introduction............................................................................................................ 125
7.1.2 Linear Mathematical Model ................................................................................. 127
7.1.3 Identification Procedure and Least Squares Method ....................................... 130
7.1.4 Experimental Setup and Data Processing .......................................................... 134
7.1.5 Results and Discussion ......................................................................................... 136
x
7.1.6 Summary ................................................................................................................ 143
7.2 Control Application ............................................................................................... 143
7.2.1 Introduction............................................................................................................ 143
7.2.2 Control Algorithm ................................................................................................. 144
7.2.3 Simulation Results ................................................................................................. 147
7.3 Summary ................................................................................................................ 151
CHAPTER 8 ..................................................................................................................................... 153
CONCLUSIONS AND FUTURE WORK ................................................................................... 153
8.1 Summary of the Completed Works .................................................................... 154
8.2 Main Findings and Conclusions .......................................................................... 156
8.3 Significance of the Research ................................................................................. 159
8.4 Future Research ..................................................................................................... 160
References ........................................................................................................................................ 164
Appendix A ...................................................................................................................................... 177
Appendix B ...................................................................................................................................... 181
xi
LIST OF FIGURES
Chapter 1
Figure 1.1. The cooperation of various systems in the study of marine science. ........................ 3
Figure 1.2. Remotely Operated Vehicle (left) and Autonomous Underwater Vehicle (right).... 4
Figure 1.3. An AUV in docking mission (left) and an AUV in inspection mission (right). ....... 6
Figure 1.4. The Collective and Cyclic Pitch Propeller CCPP. ........................................................ 6
Figure 1.5. Gavia class AUV. Courtesy of Teledyne Marine. ......................................................... 8
Chapter 2
Figure 2.1. REMUS class AUV. Courtesy of Kongsberg Maritime. ............................................. 15
Figure 2.2. Mares (Cruz and Matos, 2008) and Delphin 2 AUV (Philips et al., 2013). .............. 17
Figure 2.3. Slocum glider. Courtesy of Teledyne Marine. ............................................................ 18
Figure 2.4. Preswirl Propulsor (Huyer et al., 2012). ...................................................................... 20
Figure 2.5. AUV water-jet propulsion system (Xin et al., 2013). .................................................. 21
Figure 2.6. The Collective and Cyclic Pitch Propeller CCPP Prototype. .................................... 23
Figure 2.7. A cross section drawing of the CCPP (Humphrey, 2005). ........................................ 24
Figure 2.8. Collective Pitch Setting of CCPP. ................................................................................. 25
Figure 2.9. Cyclic Pitch Setting of CCPP. ........................................................................................ 26
Chapter 3
Figure 3.1. Coordinate system.......................................................................................................... 31
Figure 3.2. Euler’s Angle Transformation. ..................................................................................... 33
Figure 3.3. Two types of the control surface configuration. ......................................................... 40
Figure 3.4. Gavia Propulsion system............................................................................................... 41
xii
Chapter 4
Figure 4.1. Gavia AUV propeller. .................................................................................................... 56
Figure 4.2. Propeller attached into an adaptor............................................................................... 56
Figure 4.3. The towing tank at AMC-UTAS. .................................................................................. 58
Figure 4.4. Propeller Open Water Dynamometer. ......................................................................... 58
Figure 4.5. Internal assembly of Propeller Open Water Dynamometer. .................................... 59
Figure 4.6. The experimental setup of Propeller Open Water Test. ............................................ 59
Figure 4.7. Gavia AUV propeller open water diagram. ............................................................... 62
Figure 4.8. Comparison of different polynomial regression models with measured
experimental data for thrust coefficient T
C . .................................................................................. 63
Figure 4.9. Comparison of different polynomial regression models with measured
experimental data for torque coefficient Q
C . ................................................................................. 63
Figure 4.10. Comparison of different Fourier series regression models with measured
experimental data for thrust coefficient T
C . .................................................................................. 66
Figure 4.11. Comparison of different Fourier series regression models with measured
experimental data for torque coefficient Q
C . ................................................................................. 67
Chapter 5
Figure 5.1. The experimental apparatus. ........................................................................................ 73
Figure 5.2. The Experimental setup in the Towing Tank.............................................................. 74
Figure 5.3. The internal and external force balances. .................................................................... 75
Figure 5.4. The internal force transducer calibration stand. ........................................................ 76
Figure 5.5. Effect of Collective Pitch Angle Settings to T
K and Q
K . .......................................... 80
Figure 5.6. Effect of horizontal cyclic pitch angle settings. .......................................................... 81
Figure 5.7. Effect of Vertical Cyclic Pitch Angle Settings. ............................................................. 82
Figure 5.8. Effect of collective and horizontal cyclic pitch angle settings. ................................. 83
Figure 5.9. Effect of collective and vertical cyclic pitch angle settings. ...................................... 84
xiii
Figure 5.10. Effect of positive collective pitch angle settings. ...................................................... 85
Figure 5.11. Effect of negative collective pitch angle settings. ..................................................... 86
Figure 5.12. Maximum open water efficiency of CCPP in the range of advance coefficient. .. 87
Figure 5.13. Effect of horizontal cyclic pitch angle settings. ........................................................ 88
Figure 5.14. Effect of vertical cyclic pitch angle settings............................................................... 89
Chapter 6
Figure 6.1. The layout of the AUVSIPRO Simulink Model. ......................................................... 94
Figure 6.2. The Signal Builder block as the input signal in the propulsion component. ......... 94
Figure 6.3. The Lookup Table block representing the CCPP system mathematical model. .... 95
Figure 6.4. Acceleration Test. ............................................................................................................ 97
Figure 6.5. Stopping Test................................................................................................................... 98
Figure 6.6. Turning Circle Manoeuvre Test. ................................................................................... 99
Figure 6.7. Static Turning Manoeuvre Test. .................................................................................. 100
Figure 6.8. Zig-Zag Manoeuvre Test. ............................................................................................ 101
Figure 6.9. Depth-Changing Manoeuvre Test. ............................................................................. 102
Figure 6.10. Meander manoeuvre test. .......................................................................................... 102
Figure 6.11. Spiral Manoeuvre Test. .............................................................................................. 103
Figure 6.12. The travel distance of an AUV with FPP in the acceleration simulation test. .... 106
Figure 6.13. The forward speed of an AUV with FPP in the acceleration simulation test. .... 107
Figure 6.14. The travel distance of an AUV with CCPP at 50% collective pitch setting in the
acceleration simulation test. ........................................................................................................... 107
Figure 6.15. The forward speed of an AUV with CCPP at 50% collective pitch setting in the
acceleration simulation test. ........................................................................................................... 108
Figure 6.16. The travel distance of an AUV with CCPP at 100% collective pitch setting in the
acceleration simulation test. ........................................................................................................... 108
xiv
Figure 6.17. The forward speed of an AUV with CCPP at 50% collective pitch setting in the
acceleration simulation test. ........................................................................................................... 109
Figure 6.18. The stopping distance versus propeller RPM for the AUV with FPP in the
stopping simulation test. ................................................................................................................ 111
Figure 6.19. The stopping time versus propeller RPM for the AUV with FPP in the stopping
simulation test. ................................................................................................................................. 111
Figure 6.20. The stopping distance versus cyclic angle for the AUV with CCPP in the
stopping simulation test. ................................................................................................................ 112
Figure 6.21. The stopping time versus cyclic angle for the AUV with CCPP in the stopping
simulation test. ................................................................................................................................. 112
Figure 6.22. The turning diameter versus deflection angle for the AUV with FPP. ............... 113
Figure 6.23. The turning diameter versus cyclic angle for the AUV with CCPP. ................... 114
Figure 6.24. Zigzag test of AUV equipped with FPP and CCPP. .............................................. 117
Figure 6.25. The depth change simulation data for the AUV with FPP. .................................. 119
Figure 6.26. The depth change simulation data for the AUV with CCPP. ............................... 120
Chapter 7
Figure 7.1. Summary of the proposed identification procedure. .............................................. 131
Figure 7.2. Experimental location. ................................................................................................. 135
Figure 7.3. Gavia AUV performing designed manoeuvrability. ............................................... 135
Figure 7.4. Comparison between the predicted (solid line) and measured (dash lines) angular
accelerations for lateral subsystem. ............................................................................................... 137
Figure 7.5. Comparison between the predicted (solid lines) and measured (dash lines)
angular accelerations for longitudinal subsystem. ..................................................................... 137
Figure 7.6. Comparison between the predicted (solid lines) and measured (dash lines) yaw
angular acceleration for the lateral subsystem. ........................................................................... 138
xv
Figure 7.7. Comparison between the predicted (solid lines) and measured (dash lines) pitch
angular accelerations for the longitudinal subsystem. ............................................................... 138
Figure 7.8. Comparison between the simulated (solid lines) and measured (dash lines)
angular velocity yawrate for lateral subsystem. .......................................................................... 140
Figure 7.9. Comparison between the simulated (solid lines) and measured (dash lines)
angular velocity pitchrate for the longitudinal subsystem ........................................................ 140
Figure 7.10. The lawn mower pattern. .......................................................................................... 147
Figure 7.11. Depth control using the LQR. ................................................................................... 148
Figure 7.12. Pitch angle variation in the depth control. .............................................................. 149
Figure 7.13. Input cyclic angle of the CCPP. ................................................................................ 149
Figure 7.14. Heading control using the LQR. .............................................................................. 150
Figure 7.15. Input cyclic angle of the CCPP. ................................................................................ 151
xvi
LIST OF TABLES
Chapter 2
Table 2.1. Fundamental specifications of tested propeller. .......................................................... 24
Chapter 3
Table 3.1. Standard Notation for Underwater Vehicle Motion. ................................................... 30
Chapter 4
Table 4.1. Definition of four quadrants ........................................................................................... 48
Table 4.2. Fundamental specifications of tested propeller. .......................................................... 57
Table 4.3. Towing tank dimensions. ................................................................................................ 57
Table 4.4. The relationship between and J in the four quadrants. ....................................... 60
Table 4.5. Statistical properties for polynomial regression. ......................................................... 65
Table 4.6. Statistical properties for Fourier series regression. ...................................................... 67
Table 4.7. The Fourier series regression function coefficients. ..................................................... 69
Chapter 5
Table 5.1. The force balance axis system. ........................................................................................ 75
Chapter 7
Table 7.1. Assumptions in horizontal and vertical planes. ......................................................... 128
Table 7.2. Identified parameters for longitudinal and diving subsystems............................... 142
xvii
NOMENCLATURE
OA Frontal area
B Buoyancy Force
CB Centre of Buoyancy
CG Centre of Gravity
TC Thrust coefficient in four-quadrant model
QC Torque coefficient in four-quadrant model
d Diameter
F Total force
J Advance coefficient
xI Mass moment of inertia about the x axis
yI Mass moment of inertia about the y axis
zI Mass moment of inertia about the z axis
K Moment about the x axis or rolling moment
TK Thrust coefficient
QK Torque coefficient
l Length of the vehicle
M Moment about the y axis or the pitching moment
m mass of the vehicle
N Moment about the z axis or the yawing moment
n Rotational speed
p Angular velocity component about the x axis
xviii
p Angular acceleration component about the x axis
Q Torque
q Angular velocity component about the y axis
q Angular acceleration component about the y axis
r Angular velocity component about the z axis
r Angular acceleration component about the z axis
U Total uncertainty in force measurement
t Time value
u Velocity component in direction of x axis (surge)
u Acceleration component in direction of x axis
v Velocity component in direction of y axis (sway)
v Acceleration component in direction of y axis
W Total weight of AUV
w Velocity component in direction of y axis (heave)
w Acceleration component in direction of z axis
X Force in the x axis
x Displacement in the x axis
x Rate of change of displacement in the x axis
Bx The location of CB in x axis
Gx The location of CG in x axis
Y Force in the y axis
y Displacement in the y axis
y Rate of change of displacement in the y axis
By The location of CB in y axis
Gy The location of CG in y axis
Z Force in the z axis
xix
z Displacement in the x axis
z Rate of change of displacement in the z axis
Bz The location of CB in z axis
Gz The location of CG in z axis
SSE Sum of Squares due to Error
RMSE Root Mean Squared Error
2R Coefficient of determination
Greek Symbol
Roll angle of the AUV
Roll rate
Pitch angle of the AUV
Pitch rate
Yaw angle of the AUV
Yaw rate
Advance angle
Control surface deflection angle
col CCPP collective angle
cyc CCPP cyclic angle
RBτ External rigid body force
Sτ Hydrostatic force
Hτ Hydrodynamic force
propτ Propulsion force
Density of the surrounding fluid
g Acceleration due to gravity
xx
Efficiency
Volume
xxi
ABBREVIATIONS
AMC Australian Maritime College
ASV Autonomous Surface Vehicle
AUV Autonomous Underwater Vehicle
CCPP Collective and Cyclic Pitch Propeller
CFD Computational Fluid Dynamic
DAQ Data Acquisition system
DOF Degree of Freedom
EFD Experimental Fluid Dynamic
FPP Fixed Pitch Propeller
IMO International Maritime Organisation
ITTC International Towing Tank Conference
LQR Linear Quadratic Regulator
LS Least Square
PID Proportional-Integrate-Derivative
ROV Remote Operated Vehicle
SNAME Society of Naval Architects and Marine Engineers
xxii
SI System Identification
UAV Unmanned Aerial Vehicle
UTAS University of Tasmania
UUV Unmanned Underwater Vehicle
1
CHAPTER 1
Introduction
Chapter 1 provides the context for the thesis, briefly discussing the field of underwater vehicle
propulsion system. The motivation, scope of the research, contribution to research, outline of
the thesis, and publications are presented in this chapter.
Chapter 1. Introduction
2
1.1 Motivation
About 70% of the Earth’s surface is covered with water and its influence is crucial to all aspects.
The past half-century of oceanographic research has demonstrated that the ocean and seafloor
hold the keys to understanding many of the processes responsible for shaping our planet (Steele
et al., 2009). The explorations of marine environment have been providing valuable knowledge
to many fields of science and engineering.
With the assistance of the robotic systems and their advancements, it is possible to reach the
most extreme and remote area on the Earth. Compared to manned underwater vehicles and
human divers, the robotic systems are safer and more efficient. The marine robotics have expe-
rienced tremendous growth for various scientific, civilian and military applications. These ap-
plications include three main categories: inspection and surveying; search and rescue; surveil-
lance and security. Different robotic platforms have been deployed in the study of marine sci-
ence and engineering including the Unmanned Aerial Vehicle (UAV), Autonomous Surface Ves-
sel (ASV), and Unmanned Underwater Vehicle (UUV), as shown in Figure 1.1.
Among these robotic systems, UUVs have been the focus for many researchers and are becoming
more attainable for a variety of underwater missions. The UUVs represent a rapid growth with
the potential widespread deployment that will have a significant impact in the future. The recent
development requires the underwater vehicles being capable of accomplishing more complex
and advanced missions in various challenging operational environments; for example, under
ice explorations, deep-ocean floor surveys and industrial subsea infrastructure inspections
(Roberts and Sutton, 2006; Roberts and Sutton, 2012).
Based on the designed tasks and modes of operations the UUVs are categorised as Remotely
Operated Vehicle (ROV) and Autonomous Underwater Vehicle (AUV). The ROVs typically have
open frame structure, operate in limited space with human control via a tether on the surface
Chapter 1. Introduction
3
ship; whereas the AUVs normally have torpedo shape and are able to manoeuvre autonomously
without constant real-time control from operator. AUVs can operate freely with the missions
and control strategy configured in advance. They are widely used in ocean engineering and are
designed to be efficient for the long-range and large-scale survey missions. The application of
AUVs in acquisition of remotely-sensed data includes benthic habitat mapping, marine geology,
fisheries assessment, turbulent water columns and polar region continental shelf mapping
(Lucieer and Forrest, 2016). AUVs may be divided into small AUVs and large AUVs. Small AUVs
may be handled manually and operated from small boats and from shoreline. Large AUVs may
weigh up to several tons and require a research vessel with a dedicated launch and recovery
systems (Ludvigsen and Sørensen, 2016). The application of AUV technology has grown stead-
ily over the last few decades, with particularly rapid growth in the last decade (Nicholson and
Healey, 2008).
Figure 1.1. The cooperation of various systems in the study of marine science.
Chapter 1. Introduction
4
In the AUV development, besides the modern control system design and configuration modifi-
cation, the design of advanced propulsion system is of great interest to facilitate new applica-
tions. The requirements for increased manoeuvrability and functionality have started to pose a
significant impact on the research to improve the current propulsion systems. In this research
context, the propulsion system is considered as the propulsor, which converts the energy from
the power source into the thrust and manoeuvring forces. Depending on the tasks and missions,
different propulsion systems are considered. The torpedo shaped AUV typically consists of the
conventional propulsion system with the main fixed pitch propeller (FPP) providing thrust and
a set of movable control surfaces generating manoeuvring forces. Originally, for this type of
AUV, the main concern with regards to the operation is simply conducing the survey mission.
The conventional propulsion system has been improved to facilitate this traditional mission. The
manoeuvring control accuracy and the optimised efficiency provided by the propulsion system
is essential for the successful completion of an AUV mission. Despite the advantages of FPP,
there are some downsides to their use in AUVs. In recent applications, this type of propulsion
system has been revealing the shortcoming of insufficient low-speed manoeuvrability since
AUV control surface manoeuvring forces are only generated when the vehicle is moving. These
control surfaces are similar to the aircraft’s wings, rudders and elevators, which are effective as
long as they are in motion.
Figure 1.2. Remotely Operated Vehicle (left) and Autonomous Underwater Vehicle (right).
(Courtesy of Teledyne Marine).
Chapter 1. Introduction
5
It is obvious that the low speed manoeuvring performance is also important in AUV operations,
especially in the docking and intervention missions. For example, the underwater docking for
AUV is preferable since it would be very expensive and time consuming to launch and recover
the AUV on board the mother ship after each mission. Docking has been identified as an ena-
bling capability to support off-board operation of AUVs from submarines, autonomous surface
vessels, other AUVs, ships, and under ice (Bellingham, 2016). The AUV must have the low speed
manoeuvrability to approach the target and connect precisely to the docking platform. In the
intervention application at hovering state, the AUV utilises the robotic arm or the manipulator
for the sample collection in the environment that they are operating. There have been recent
developments and breakthroughs in the underwater manipulator technologies for AUVs (so
called autonomous manipulator) (Kim et al., 2016). The most recent effort is the Trident FP7 EU
research project funded by the European Commission (Kim et al., 2016; Sanz et al., 2012). Fur-
thermore, many underwater applications, such as marine observation and environmental as-
sessment, require stationary observation at low speed. For a number of data collection opera-
tions, it is desirable to be able to deploy an AUV which can travel to a predetermined location,
station itself in the water column at this location while recording environmental data over an
extended time frame and then return to a recovery location (Briggs et al., 2010). In these missions,
the AUV with conventional propulsion is inefficient due to the limitation of the control surfaces
at zero or low speed operation regime. In general, there is limited access to AUVs with station
keeping/hovering capabilities and this is at present the situation for AUVs with manipulator
capabilities doing light intervention and sampling (Ludvigsen and Sørensen, 2016) . The current
desirable characteristics of an AUV platform are cruising at medium to high speed in the survey
missions, station keeping, and manoeuvring at low speed. This thesis has been motivated by the
desire for an alternative propulsion system of a high manoeuvring AUV to be operated not only
at cruising speed but also at low speed.
Chapter 1. Introduction
6
Figure 1.3. An AUV in docking mission (left) and an AUV in inspection mission (right).
The Collective and Cyclic Pitch Propeller (CCPP) to assist the low-speed operations of an AUV
has been the subject of this research. The key difference between the CCPP and conventional
system is the use of one integrated system instead of the FPP and control surfaces for propulsion
and manoeuvring control. The CCPP has the ability to generate thrust and manoeuvring forces
simultaneously. This feature of CCPP offers the unique and undistinguished capability.
Figure 1.4. The Collective and Cyclic Pitch Propeller CCPP.
The National Centre for Maritime Engineering and Hydrodynamics at Australian Maritime Col-
lege, University of Tasmania (UTAS) has been studying the CCPP system aiming to improve the
AUV overall performance for complex mission tasks. CCPP has been one of the most innovative
Chapter 1. Introduction
7
propulsion systems designed and applied to an AUV. This is in contrast to aerial vehicle such as
helicopter where the use of variable pitch systems is commonplace. Hence, there is an important
need for a research into the viability of this alternative propulsion system and this is the moti-
vation for this thesis.
1.2 Scope of the Thesis
The primary objective of the research project is to investigate the potential of the CCPP as the
propulsion system of choice for a torpedo shaped AUV. In this thesis, the main research question
was that: “Does the AUV equipped with CCPP have better manoeuvrability than the AUV with
FPP”. This thesis looked into the determination of the more applicable propulsion system for
AUVs by numerically comparing the performance of an AUV equipped with CCPP to the con-
ventional FPP. To address the research goal and answer the research question, a methodology
was developed in which both experimental and numerical approaches were utilised.
Experimental approach consisted of the experimental study of the CCPP and FPP in the towing
tank test. The hydrodynamic characteristics of the CCPP were difficult to model by using the
theoretical and numerical approach due to the complexity in working principle. Hence, there
was a need to conduct an experimental study that can measure accurately the generated forces
and to construct the empirical models based on these obtained data. Two types of experiments
were conducted including the bollard pull test and model captive test. The experimental proce-
dure was based on the guideline proposed by the International Towing Tank Conference ITTC.
These model tests have been widely used to predict motions and forces in marine applications.
The CCPP empirical model was made non-dimensional and then scaled to the size of Gavia’s
FPP dimension for the comparison study. Since the CCPP was examined in the low speed oper-
ation, the scaling effect has no significant effects on its performance. The accurate modelling of
Chapter 1. Introduction
8
the propulsion systems were essential to calculate the AUV’s response to different operational
conditions and control strategies.
The use of CCPP to manoeuvre an AUV represented a challenging problem, which motivated
the need for a simulation. The complexity of manoeuvres in real life makes computer simulation
useful for their study (Lewis, 1988). In this thesis, the numerical approach consisted of establish-
ing the comprehensive mathematical model of the AUV with the hydrodynamic parameters ob-
tained from theoretical and analytical methods; constructing a numerical simulation program
called AUVSIPRO based on MATLAB/SimulinkTM; and developing the control algorithm for
AUV with CCPP. The propulsion system models and hull hydrodynamic model were incorpo-
rated in AUVSIPRO. Although validation is required, the main advantage of this approach is
that it provides a good understanding of the performance of an AUV without the need for the
physical model. In addition, as the development of an AUV is both costly and time consuming,
the use of modelling and simulations is essential to the design process.
Figure 1.5. Gavia class AUV (Courtesy of Teledyne Marine).
At the AMC-UTAS, several AUVs have been used for the research and study. In this project, the
Gavia AUV has been considered as the research platform. The CCPP has been simulated to em-
power the Gavia AUV based on the developed propulsion and vehicle model. Given the Gavia
AUV platform with the conventional FPP propulsion system and the prototype of CCPP, it has
been considered an opportunity to investigate the potential of CCPP for an AUV by conducting
the comparison study.
Chapter 1. Introduction
9
1.3 Contribution to Research
The key contributions and achievements of this work are to provide an insight into the perfor-
mance of an AUV equipped with CCPP. There had been insufficient information in the CCPP
hydrodynamic characteristics and the manoeuvrability of an AUV with CCPP had not been fully
examined. The dynamic modelling of an underwater vehicle FPP in four-quadrant operation
was also presented. The in depth comparison results for both propulsion systems CCPP and
FPP provided useful data for the researchers in selecting and designing a propulsion system for
an AUV. The knowledge of the propulsion system characteristics is necessary for the operation
of an AUV. An additional contribution of the research is to develop a controller for an AUV
equipped with CCPP. The control problem of an AUV is very challenging since the mathemati-
cal model of AUV is characterized by high nonlinearity and strongly coupling. The novel two-
stage system identification method was proposed to identify the linear mathematical model of
the Gavia AUV and the optimal linear control algorithm was successfully applied to the system.
1.4 Outline of the Thesis
The thesis documents the experimental and numerical simulation studies conducted in this re-
search project. It is divided into eight chapters as follows:
Chapter 1 provides the context for the following chapters, including the motivation, scope of
the research, outline of the thesis, contribution to research, and the publications.
Chapter 2 describes the background and a comprehensive literature review of the research pro-
ject. It introduces the reasons for interest in alternative propulsion system to the conventional
propeller applied to an AUV. A review of the state of the art of various underwater vehicle pro-
pulsion systems are presented. The advantages and disadvantages of these propulsion systems
Chapter 1. Introduction
10
are discussed in term of performance characteristics. The chapter also includes a literature re-
view regarding the previous research studies conducted on the CCPP.
Chapter 3 discusses a mathematical model for an AUV. The modelling of an AUV platform is
essential to investigate the manoeuvring characteristics of an AUV equipped with a CCPP. The
reference frames including the earth-fixed and body-fixed coordinates are defined. The model-
ling of an AUV involves the development of both kinematic and dynamic model. The analytical
and theoretical method to estimate the hydrodynamic coefficients are briefly mentioned. This
chapter lay the theoretical foundations of the works conducted in the following chapters.
Chapter 4 and Chapter 5 provide an in-depth modelling of the conventional propulsion system
FPP and the CCPP respectively using the experimental approach. Two separate testing tech-
niques and setups for the FPP and CCPP testing are considered. The experiments to examine
the hydrodynamic characteristics of both propulsion systems are conducted. The obtained data
are analysed and discussed in detail.
Chapter 6 illustrates a detailed manoeuvring simulation of an AUV equipped with FPP and
CCPP. A variety of standard manoeuvring tests for marine vehicles are considered to investigate
the AUV performance.
Chapter 7 examines the control design for an AUV equipped with CCPP. The content of this
chapter includes the two-stage identification method to define the linear model of Gavia AUV
and the optimal control development. The depth and heading control are performed to validate
the controller.
Chapter 8 presents an overview of the works conducted in the research project, summaries the
main findings, emphasises the significance of the study, and provides the suggested direction
for the continued investigation in light of the current works.
Chapter 1. Introduction
11
1.5 Publications
Parts of the thesis have been submitted and published in the following papers in the past three
years during the course of the research project.
1.5.1 Presentations and Conference Papers
Minh Tran, Hung Nguyen, Jonathan Binns, Shuhong Chai and Alex Forrest, A Study of new
propulsion system for an Autonomous Underwater Vehicle, 9th Graduate Research Conference
at the University of Tasmania, Hobart, Australia, 2015.
Minh Tran, Supun A.T. Randeni, Hung D. Nguyen, Jonathan Binns, Shuhong Chai and Alex
Forrest, Least Squares Optimisation Algorithm Based System Identification of an Autono-
mous Underwater Vehicle, Proceedings of the 3rd Vietnam Conference on Control and Automation,
Vietnam, 2015.
Minh Tran, Hung Nguyen, Jonathan Binns, Shuhong Chai and Alex Forrest, AUVSIPRO–A
Simulation Program for Performance Prediction of Autonomous Underwater Vehicle with
Different Propulsion System Configurations. International Conference on Modelling and Simu-
lation for Autonomous Systems. Springer, 72-82.
Minh Tran, Hung Nguyen, Jonathan Binns, Shuhong Chai and Alex Forrest, Optimal control
of an autonomous underwater vehicle equipped with the collective and cyclic pitch propel-
ler. Control Conference (ASCC), 2017 11th Asian. IEEE, 354-359.
1.5.2 Journal Papers
Minh Tran, Hung Nguyen, Jonathan Binns, Shuhong Chai and Alex Forrest, A practical ap-
proach to the dynamics modelling of an underwater vehicle propeller in all four quadrants
of operation, Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineer-
ing for the Maritime Environment. (Published).
Chapter 1. Introduction
12
Minh Tran, Hung Nguyen, Jonathan Binns, Shuhong Chai and Alex Forrest, Experimental
Study of the Collective and Cyclic Pitch Propeller, The Journal of Marine Science and Applica-
tion. (Accepted for publication).
Minh Tran, Hung Nguyen, Jonathan Binns, Shuhong Chai and Alex Forrest, A comparison
study of two propulsion system configurations for an autonomous underwater vehicle,
Ocean Engineering, An International Journal of Research and Development. (In progress).
13
CHAPTER 2
Literature Review
This chapter describes the background and literature review of the research project. It introduces
the reasons for interest in an alternative propulsion system to the conventional propeller applied
to an AUV. In this chapter, a review of the state of the art of various underwater vehicle propul-
sion systems are presented. The advantages and disadvantages of these propulsion systems are
discussed in term of performance characteristics. The chapter concludes with the literature re-
view of previous research conducted for CCPP propulsion system.
Part of this chapter has been published in the “Proceeding of 9th Graduate Research Conference at the
University of Tasmania”. The citation for the presentation is:
Minh Tran, Hung Nguyen, Jonathan Binns, Shuhong Chai and Alex Forrest, A Study of new
propulsion system for an Autonomous Underwater Vehicle, 9th Graduate Research Conference at
the University of Tasmania, Hobart, Australia, 2015.
Chapter 2. Literature Review
14
2.1 Introduction
AUVs play a critical role in the maritime industry to provide automated missions. AUV tech-
nology is a fast growing research area with a wide range of subsystems being developed. One
of the key challenges each AUV experience, is achieving an accurate manoeuvrability. Essen-
tially, a basic consideration for the design of swimming machines is the design of propulsors:
their shape, location on the robot, mechanical properties (e.g., inertia and stiffness), and pattern
of movement (Colgate and Lynch, 2004). In this chapter, the conventional propulsion system for
a torpedo shaped underwater vehicle and its performance characteristics are presented. In ad-
dition, a comprehensive literature study is mentioned to describe the relevant propulsion sys-
tems with different configurations as alternative propulsion system to the conventional one. A
brief description and performance analysis of these propulsion systems are conducted, discuss-
ing the advantages and disadvantages of using these systems. Finally, the CCPP configuration
is briefly explained and the previous works related to the research of CCPP is reviewed.
2.2 Conventional propulsion system for an autonomous underwater vehicle
and its limitations
2.2.1 Conventional propulsion system with Fixed Pitch Propeller (FPP)
In modern subsea mapping and surveying applications, AUVs are usually designed for high
speed cruising so that the vehicles are able to cover the longer distance and larger range of in-
spection area from several meters to hundreds of meters. A majority of work related to propul-
sion system has been conducted on the traditional propeller-driven propulsion.
The use of a FPP at the aft end combined with control surfaces as means of propulsion are prev-
alent for underwater vehicles, especially for torpedo-shaped AUVs, such as HUGIN 1000 class
(Hagen et al., 2003), Autosub 6000 (McPhail, 2009) and REMUS 600 class (Stokey et al., 2005). In
Chapter 2. Literature Review
15
this conventional configuration, the FPP provides thrust for AUV while the manoeuvring of an
AUV is achieved through adjustment of the control surfaces. Additionally, the ducted propellers
are also utilised to increase the propulsion system efficiency of AUVs, including AUV PreToS
(Chakrabarti et al., 2014) and Gavia class (Hiller et al., 2012).
Figure 2.1. REMUS class AUV. (Courtesy of Kongsberg Maritime).
2.2.2 Limitations of the conventional propulsion system
It is essential that the control surfaces be capable of generating manoeuvring forces that are
sufficient in magnitude and oriented in desired control directions. However, these traditional
types of propulsion system have the shortcoming of insufficient low-speed manoeuvrability be-
cause low aspect ratio control surface characteristics significantly limit their effectiveness
(Huyer et al., 2010; Farnsworth et al., 2010). With the exception of thrust from the propeller,
AUV control surface manoeuvring forces are only generated when the vehicle is in motion at
sufficient speed. Hence, the AUV missions at zero and low speed are limited.
The control surfaces and other appendages protruding from the hull can be damaged when the
vehicle travelling in a confined environment. They are also easily to be affected by the environ-
mental disturbances and turbulence. In such a condition, the control surfaces are not able to
produce enough forces and moments to counteract the influences resulted from strong ocean
currents. In term of efficiency, the lack of variable pitch capability of the conventional propeller
leads to AUV propulsion having relatively low efficiency at different operational conditions. For
these reasons, there is an important need for research into the alternative propulsion system for
Chapter 2. Literature Review
16
AUV, which could increase the functionality and manoeuvrability at different operational
speeds and missions. The aim of the next generation of AUVs is also to be able to combine long
range survey capabilities with low speed investigation of the environment encountered (Palmer,
2009). For example, with the growing acceptance of survey-class AUVs in the commercial sector,
interest is growing in the use of AUVs for activities such as periodic inspection of subsea equip-
ment installations and the use of AUVs for maintenance and repair activities (Bellingham, 2016).
In addition, the underwater docking represent a major challenge in the design and improvement
of current AUV propulsion.
2.3 Alternative Propulsion Systems for an Underwater Vehicle
There are already various concepts of propulsion systems, which have been designed and ap-
plied to an underwater vehicle as the solution to the downsides of a conventional FPP. These
following sections describe some of the prevalent types with their specific mechanisms and
unique performance capabilities. The purpose is to give an overview of the current state of re-
search in the fields related to underwater vehicle propulsion system.
2.3.1 Thruster
To enhance the low speed manoeuvrability, the thrusters are utilised and positioned at different
locations around the AUV without changing the low drag profile of the torpedo-shaped AUV.
The thrusters are categorised into two main different types: through-body thrusters (tunnel
thrusters) and the external thrusters. Adding thrusters enables the vehicle to travel long dis-
tances at high speeds to a desired destination and then perform tasks that require low speed
manoeuvrability (Saunders and Nahon, 2002). Thruster is the standard choice in propelling low
speed AUV and is widely used in turbulent environment since its generated forces and moments
are generally independent of surrounding fluid. A number of these AUVs have been developed,
including Typhoon (Allotta et al., 2015), Delphin2 (Philips et al., 2013), C-Scout (Saunders and
Chapter 2. Literature Review
17
Nahon, 2002), Odyssey (Eskesen et al., 2009), and Mares (Cruz and Matos, 2008). The propeller
based thrusters have been employed for low speed control due to their reliability, responsive-
ness and ability to generate forces throughout the operational range of the vehicle (Palmer, 2009).
Figure 2.2. Mares (Cruz and Matos, 2008) and Delphin 2 AUV (Philips et al., 2013).
However, the disadvantage of using thrusters is the reduced propulsive efficiency at high speeds.
Tunnel thrusters could increase the parasitic drag of the vehicle and also take up considerable
volume that could otherwise be used for energy or payload (Huyer et al., 2010). Hence, the in-
ternal architecture of the AUV using tunnel thrusters are quite complex. Moreover, the external
thrusters are vulnerable to the damage and corrosion since they are subject to high influx of
water. A number of thrusters installed in close proximity result in the cross-coupling interac-
tions influencing the control characteristics considerably (Russell and Bellec, 1981).
2.3.2 Vectored Thruster
An alternative to the conventional propeller that could improve the manoeuvrability and effi-
ciency of underwater vehicles is the vectored thruster propeller, or a steerable propeller. The
vectored thrusters are a special type of the thrusters. The vectored thruster propellers applied
to underwater vehicle are inspired from the azimuthing podded propulsion system for ships
(Stettler, 2004). In the vectored thruster configuration, the generated force and moment are con-
Chapter 2. Literature Review
18
trolled by actively altering the thruster direction. In spite of the mechanical complexity, the ad-
vantages of using vectored thruster propeller for propulsion system of AUV include improved
manoeuvrability, and the fact that fewer fins, which may snag on underwater cables or other
obstacles in a confined environment, protrude from the vehicle (von Ellenrieder and Ackermann,
2006). The vectored thruster propulsion for underwater vehicle is still under development and
has not been applied in practical application.
2.3.3 Buoyancy Engine
To increase the hover capability of the conventional torpedo shaped AUV, researchers have
come up with some modifications to the propulsion system by taking advantage of the balance
between buoyancy and hydrodynamic forces by changing the ballast mass to drive it in water
(Abraham and Yi, 2015). A review for popular buoyance engines which mainly used for the
underwater gliders could be found in reference (Ullah et al., 2015). Autonomous large area sur-
veys of ocean are currently carried out using either flight-style propeller-driven AUVs or gliders
(Furlong et al., 2007). The endurance of glider is significantly longer than the traditional AUV.
The power requirement for gliders are substantially low in the comparison to the propeller-
driven AUVs. A detailed discussion on the current studies of the gliders could be found in the
following reference (Jenkins and D’Spain, 2016).
Figure 2.3. Slocum glider. (Courtesy of Teledyne Marine).
Chapter 2. Literature Review
19
The glider is an effective tool in measuring water column parameters. However, the accuracy in
navigation and manoeuvring is limited (Ludvigsen and Sørensen, 2016). The produced thrust
from buoyancy engine is not sufficient compared to other types of propulsion system resulting
in the gliders instability to environmental disturbances. Hence, the gliders are not able to oper-
ate in the strong ocean currents. Moreover, due to the nature of their propulsion system gliders
are restricted to seesaw flight profiles (Furlong et al., 2007).
2.3.4 Biomimetic propulsion
Researchers also look to nature as an inspiration for their design where the biomimetic propul-
sion system has been considered (Mazlan and Naddi, 2015). Nature preserve various means of
underwater propulsion. Different species display a multitude of propulsion and manoeuvring
methods appropriate for their environment (Riggs, 2010). Research on aquatic animals has in-
creased and these animals have been mimicked to improve underwater vehicles and their loco-
motion mechanisms for better performance (Korkmaz et al., 2015). The most popular types of
biomimetic propulsion system are the flapping foil (flexible fins) and the oscillating paddle
(rigid paddles). Creatures with the large ratio of body weight to surface are normally propel
themselves by flapping their wings continuously while natural species with the small ratio of
body weight to area swim propelled by transferring momentum to water with the mechanism
similar to jet propulsion. The swimming animals share some of similar mechanisms with flying
animals but the fundamental nature of generated thrust is different. The primary goal in flying
is the continuous production of steady lift, to balance the large body weight within a medium
with small density. The major goal in fish swimming is to minimize drag forces within a medium
a thousand times more dense than air—the generation of steady lift to support the (small) net
weight is of secondary or no importance at all (Triantafyllou et al., 2004). The biomimetic pro-
pulsion is not dangerous to surrounding objects, animals and humans compared to conventional
Chapter 2. Literature Review
20
propeller and other rotating propulsions. Biomimetic propulsion also offers some distinct ad-
vantages such as excellent manoeuvrability for steering and low-noise operation, but is consid-
ered not propulsive efficiency (Korde, 2004). Although there exist solutions on the efficiency
issues, there are many challenges to overcome related to the mechanical design. The mechanism
of current biomimetic propulsions are still complex and hard to control. Considerable efforts
have been put into the investigation of biomimetic propulsion to decrease its power consump-
tion and increase functionality (Read, 2001; Watts, 2009; Roper et al., 2011; Polidoro, 2003;
Hubbard et al., 2014). Solving these issues will greatly facilitate the development of underwater
marine robotics.
2.3.5 Preswirl Propulsor
Another concept of underwater propulsion is the preswirl propulsor. This propulsor has been
designed with the intention to overcome the limitation of the conventional FPP. This novel pro-
pulsor utilises an upstream stator row, where the individual stator blade pitch angles can be
varied, coupled with a downstream rotor. By sinusoidally varying the individual stator blade
pitch angles around the circumference, the upstream stator row produces a significant side force
(Huyer et al., 2012; Huyer et al., 2010; Farnsworth et al., 2010). The prototype of preswirl pro-
pulsor has been successfully tested but its application to an AUV has not been reported.
Figure 2.4. Preswirl Propulsor (Huyer et al., 2012).
Chapter 2. Literature Review
21
2.3.6 Jet-pump or waterjet Propulsion
In the jet-pump or waterjet propulsion, the water is absorbed into the water hydraulic pump
from the bow section of the AUV. After being pressurised, the water jets out of the nozzle and
generates reaction thrust (Xin et al., 2013). The yaw and pitch manoeuvres are performed by
either the differential thrust mechanism or the waterjet steering system.
Using jet-pumps for propulsion and steering is an alternative option to the conventional propel-
ler-driven propulsion. Pump and jet systems are less energy efficient with respect to blade pro-
pellers and rudder steering (Alam et al., 2014). The jet-pump also offers several advantages from
the point of view of the mechanical design (absence of rotating parts and transmission mecha-
nisms), realization cost (simpler fibre-class cover), robustness with respect to transportation/de-
ployment/recovery damages (no appendixes protruding from the cylinder), safety of occasional
swimmers in proximity of the vehicle (jet-pumps are much less likely to cause harm at low speed
with respect to propeller blades) (Alvarez et al., 2009). The investigations and studies of jet-
pump propulsion for AUVs have been examined thoroughly in the literature (Korde, 2004;
Polsenberg Thomas, 2007; Mohseni, 2006). However, the waterjet propulsion are generally not
used for medium-speed and high speed applications due to the decrease in efficiency. The con-
trol accuracy of waterjet propulsion is limited in the underwater environment in which the six
degree-of-freedom manoeuvrability is required.
Figure 2.5. AUV water-jet propulsion system (Xin et al., 2013).
Chapter 2. Literature Review
22
2.3.7 Hybrid Propulsors
There are a number of AUVs integrating different methods of locomotion in one system. The
hybrid propulsion system have been extensively studied as a potential means for improvement
of underwater vehicle performance. An excellent example of this can be seen on the Tethys-class
AUV built by the Monterey Bay Aquarium Research Institute. The Tethys-class AUV has a
unique ability to operate efficiently in three different operational modes with a range of actua-
tors: traditional propeller for high speed, a moving internal mass (like a glider) for low speed,
and variable buoyancy for drifting (like a float) (Hobson et al., 2012). The Guanay-II AUV uses
the propulsion system comprises: a main engine, which provides the propulsion, two side
thrusters, which monitor the direction of the vehicle and an internal pneumatic stainless cylin-
der, which allows the vehicle to dive by taking in and ejecting water (Gomáriz et al., 2015). An-
other hybrid AUV uses ducted propeller and rudder located at the aft for horizontal motion and
internal mass shifter mechanism for vertical motion (Tran et al., 2015b) or the internal rolling
mass mechanism for roll control (Hong and Chitre, 2015). The internal actuators are located
inside the vehicle hull and hence are less subject to damage than the external thrusters are. How-
ever, the use of moving internal actuators are limited due to the significant requirement for the
inner hull space and high power consumption from multiple systems. Additionally, it is chal-
lenging to design the control strategy for the integrated propulsion unit with different force
generation methods.
2.4 Collective and Cyclic Pitch Propeller (CCPP)
Even though a variety of improvements and innovations has been made, the development of an
advanced propulsion system for an AUV remains a challenging research area. It is essential to
develop the alternative means of propulsion system for AUVs that could increase both efficiency
and manoeuvrability. The CCPP has been developed to overcome the limitations revealed by
Chapter 2. Literature Review
23
the current propulsion configurations and to investigate its performance characteristics in un-
derwater working environment. The most attractive characteristic of CCPP is its capability to
generate continuous thrust and manoeuvring forces simultaneously. The CCPP propulsion sys-
tem has improved the underwater vehicle efficiency at cruising speed and the high degree of
manoeuvrability at low speed without using the control surfaces. This section explains its basic
configuration and reviews the development of the CCPP.
The CCPP, as shown in Figure 2.6, has the similar working principle to the conventional main
rotor of the helicopter (Seddon and Newman, 2011) and the variable vector propeller of an un-
derwater vehicle (Nagashima et al., 2006). The essential component of CCPP is a swashplate,
which is controlled by linear actuators, as shown in Figure 2.7. The swashplate enables the ad-
justment of the propeller pitch angles as the shaft is rotating. There are two primary blade set-
tings in the CCPP configuration, the collective pitch setting and the cyclic pitch setting.
Figure 2.6. The Collective and Cyclic Pitch Propeller CCPP Prototype.
Chapter 2. Literature Review
24
The main particulars of the examined model are given in Table 2.1.
Table 2.1. Fundamental specifications of tested propeller (Humphrey, 2005).
Symbol Description Value Unit
Scale 1:1
Z Number of blades 4
Blade section NACA 0012
D Diameter 0.305 m
col Collective angle -29 to 29 Degree
cyc Cyclic angle -20 to 20 Degree
Figure 2.7. A cross section drawing of the CCPP (Humphrey, 2005).
Chapter 2. Literature Review
25
The collective pitch setting of the CCPP is similar to Controllable Pitch Propeller (CPP) which is
well-known for the advantage of full power utilisation at any circumstances, such as: accelerat-
ing and stopping; rapid manoeuvring; and dynamic positioning (Dang et al., 2012). The pitch
angles of all blades could be changed simultaneously to a particular value at position 1, 2, 3 and
4 in the collective pitch setting. As shown in Figure 2.8, all the blades are increased to a defined
value. This feature allows the propulsor to alter its axial thrust without changing the propeller
rotational speed. The CPP has been studied for an AUV specially designed in the tunnel inspec-
tion mission (Jung et al., 2012). In these types of mission, the reverse thrust is crucial as the
vehicle is operating is narrow space. In addition, the ability to change the pitch angle results in
the optimised thrust from CCPP at various operating speeds. This helps the AUV reach maxi-
mum efficiency in different operations, avoid the motor to be overloaded and increase the motor
duration (Tarbiat et al., 2014).
Figure 2.8. Collective Pitch Setting of CCPP.
CCPP is primarily different from the CPP in the cyclic pitch control to create the manoeuvring
side forces. CCPP is a means of manoeuvring force generation that does not require the control
Chapter 2. Literature Review
26
surface but due to the cyclic pitch setting. The angles of each propeller blade can also be posi-
tioned periodically during a rotation in the cyclic pitch setting by manipulating the orientation
of swash plate. As shown in Figure 2.9, the blade pitch angle will be increased in position 2,
decreased in position 4; and remained neutral in position 1 and position 3 per revolution. As the
results, more lift will be created in position 2 and the side force as well as the moment are created.
Therefore, the CCPP can generate thrust, as well as manoeuvring forces and moments in differ-
ent directions. The physical parameter and dynamic model of CCPP will be presented thor-
oughly in the next chapters.
Figure 2.9. Cyclic Pitch Setting of CCPP.
Extensive research has been conducted in the aeronautics on the helicopter main rotor. However,
there has been limited publications in the literature considering the unique features of CCPP
and its applications to marine underwater vehicles. The complex mechanical design and control
system associated with this propulsion system has prevented the extensive research effort. Pre-
vious studies have focused on the mechanical design and hardware integration. The prototype
Chapter 2. Literature Review
27
of CCPP utilised in this study was initially built at Memorial University of Newfoundland, Can-
ada (Humphrey, 2005). A prototype CCPP with control system was designed, constructed and
tested. A series of initial tests were carried out to study its characteristics in the open water con-
dition. The most recent research was conducted at the Australian Maritime College, University
of Tasmania to investigate the performance of an underwater vehicle model equipped with
CCPP in straight line model captive test (Niyomka, 2014). In addition, the prediction program
for performance of CCPP was also constructed using BEMT and the Leishman-Beddoes dy-
namic stall model. Although the innovative features of CCPP for underwater vehicle were dis-
covered from previous studies its performance characteristics were not fully demonstrated yet.
Additionally, due to the lack of experimental data, the modelling and simulation studies were
not conducted in detail. Therefore, the potential application of CCPP to an AUV has not been
verified. In response to the shortcomings of previous works, the studies with underwater vehi-
cle model equipped with CCPP have been carried out thoroughly in this thesis. The analytical
method, experimental approach and numerical simulation are presented and applied in the next
chapters. The methodologies associated with these approaches are also reviewed and explained.
2.5 Summary
The background and literature review of the research project were described in chapter 2. It
introduced the reasons for interest in alternative propulsion system to the conventional propel-
ler applied to an AUV. It also presented a review of the state of the art of various underwater
vehicle propulsion systems, and more specifically, the propulsion system for the torpedo shaped
underwater vehicle. The advantages and disadvantages of these propulsion systems were dis-
cussed thoroughly in term of mechanisms and performance characteristics. Chapter 2 concluded
with a literature review of previous research conducted for the CCPP to pave way for the current
research.
28
CHAPTER 3
AUV Equations of Motion
This chapter discusses the mathematical model of an underwater vehicle. The modelling of an
AUV involves the development of both kinematic and dynamic model. The analytical and the-
oretical method to estimate the hydrodynamic coefficients are briefly presented. This chapter
provides the theoretical foundations for the further investigation conducted in the following
chapters.
Chapter 3. AUV Equations of Motion
29
3.1 Introduction
The works described in this section is concerned with mathematical modelling of the torpedo
shaped underwater vehicle. Generally, there are three modelling approaches to obtain a model
of an AUV, namely first principles modelling, grey box modelling and black box modelling. The
first principle modelling is also known as white box modelling and it is applied to derive the
comprehensive mathematical model of an underwater vehicle using the laws of mechanics and
hydrodynamics. The relevant first principle modelling approaches are Lagrangian and Newton-
Euler modelling. This method provides a comprehensive physical understanding of the vehicle
components and their interactions in the development stage.
In this thesis, the Newton-Euler modelling approach is considered. This modelling of an AUV
involves the development of both kinematic and dynamic model. The general motion of an AUV
is fully described by six degree-of-freedom equations. The non-linear hydrodynamic coefficients
of an AUV are calculated using the analytical and theoretical estimation.
An accurate vehicle dynamic model would greatly aid in the development of the simulation
program and the controller design. The objective of this chapter is to build the sufficiently high
fidelity dynamic model. The mathematical model forms the foundation for investigating the
AUV performance with different propulsions. The more precise the mathematical model repre-
senting the characteristic of an AUV is, better the performance of the simulation program.
The following assumptions are made in the modelling of the underwater vehicle:
The AUV is submerged in a homogeneous fluid;
The AUV is moving in a stationary body of water having constant properties;
Underwater currents and disturbances are neglected;
The underwater vehicle is considered as a rigid body of constant mass.
Chapter 3. AUV Equations of Motion
30
3.2 Coordinate Systems and Transformation
3.2.1 Six Degree of Freedom and Standard Notation
The underwater vehicle operates in a three dimensional space and it is convenient to describe
the state variables of the vehicle and the forces acting on it by the six independent coordinates
or six degree of freedom (6 DOF). The standard of SNAME (Society of Naval Architects and
Marine Engineers) notation is used to describe the 6 DOF quantities and is summarised in the
Table 3.1 (SNAME, 1950). In this notation, motion in the horizontal plane is referred to as surge
(steady forward motion), sway (sideway motion), and yaw (rotation about the vertical axis).
Three remaining DOFs are in the vertical plane including roll (rotation about longitudinal axis),
pitch (rotation about transverse axis), and heave (vertical motion).
Table 3.1. Standard Notation for Underwater Vehicle Motion.
DOF Motions Forces and
Moments
Translational and
Rotational Velocity
Positions and
Euler Angles
1 Surge X u x
2 Sway Y v y
3 Heave Z w z
4 Roll K p
5 Pitch M q
6 Yaw N r
By convention for underwater vehicles, the positive x direction is taken as forward, the positive
y direction is taken as to the right, the positive z direction is taken as down, and the right-
hand rule applies for angles (Hajosy, 1994).
Chapter 3. AUV Equations of Motion
31
3.2.2 Coordinate Systems
Figure 3.1. Coordinate system.
This section presents the coordinate systems used for measurement of vehicle’s position, veloc-
ity and acceleration. There are two reference frames describing the state variables of an AUV.
There Earth-fixed reference frame is selected as the inertial reference frame since the underwater
vehicles travel at low enough speeds so that the acceleration of points on the surface of the Earth
can be neglected (Hajosy, 1994). The Earth-fixed coordinate is used to represent the position and
orientation of the vehicle relative to a fixed point of the Earth. The body-fixed coordinate with
the origin ,O is usually selected to coincident with the vehicle centre of gravity CG. The Body-
Fixed Coordinate is used to describe the translational and rotational velocities.
Each axis of the coordinate system corresponds to a variable and all variables in both coordinate
systems forms the state variables of the system. The position and orientation of the vehicle rela-
tive to an Earth-Fixed Coordinate is defined as the position vector 1η and orientation vector
2η :
Tx y z 1
η (3.1)
T 2
η (3.2)
Chapter 3. AUV Equations of Motion
32
where x is the distance in the inertial north direction, y is the distance east, and z is the dis-
tance down. , , and are the Euler roll, pitch and yaw angles.
The position and orientation vectors are grouped as vector :η
Tx y z
T T
1 2η η η (3.3)
The translational velocity vector 1
Tu v w υ is defined in the body-fixed coordinate, where
surge velocity u is positive along the vehicle X axis, sway velocity v is positive along the Y
axis, and heave velocity w is positive along the vehicle Z axis. The rotational velocity vector
Tp q r 2
υ is also defined in the body-fixed coordinate, where roll rate p is right-hand
positive about the vehicle X axis, pitch rate q is right-hand positive about the Y axis, and
yaw rate r is right-hand positive about Z axis.
The translational and rotational velocities are grouped as vector :υ
T Tu v w p q r 1 2
υ υ υ (3.4)
3.2.3 Euler Angles and Vector Transformation
The two coordinate systems have a relationship that is obtained through Euler angles as shown
in Figure 3.2. The vehicle coordinate system is rotated relative to the inertial coordinate system
by first aligning the coordinate systems such that the b
X axis points north, the b
Y axis points
east, and the b
Z axis point down. The vehicle coordinate system is then rotated by the yaw
angle about the vehicle b
Z axis, denoted by 3
Z , then by the pitch angle about the result-
ing b
Y axis, denoted 2
Y , then finally by the roll angle about the resulting b
X axis, denoted
1X . The sequence of rotations is illustrated in Figure 3.2.
Chapter 3. AUV Equations of Motion
33
Figure 3.2. Euler’s Angle Transformation.
The three rotation matrices about each axis, z, y and x can be defined as:
,
cos sin 0
sin cos 0
0 0 1z
C
, y,
cos 0 sin
0 1 0
sin 0 cos
C
, x,
1 0 0
0 cos sin
0 sin cos
C
(3.5)
3.3 Kinematics
The kinematic equations represents the transformation between two coordinate systems. The
translational velocity vector υ can be mapped to the Earth-fixed coordinate by a rotation matrix
J (Fossen, 2011):
2η = J η υ (3.6)
where:
1 2
2
2 2
J η 0J η
0 J η (3.7)
The matrices 1 2J η and 2 2
J η are defined based on the Euler angle transformation as:
Chapter 3. AUV Equations of Motion
34
, , ,
T T T
z y x
c c s c c s s s s c c s
C C C s c c c s s s c s s s c
s c s c c
1 2J η (3.8)
1
0
0 / /
s t c t
c s
s c c c
2 2J η (3.9)
Note that sin is represented as s , cos as c , and tan as .t
3.4 Dynamics
3.4.1 Equations of Motion for Underwater Vehicle
The Equations of Motion (EOM) for an underwater vehicle with 6 DOF, with respect to the Body-
fixed frame are derived in this section based on assumptions from section 3.1. These equations
are useful for the simulation and the design of control system. The derivation of the EOM is
resulted from the Newton’s second law and expressed in the component form as (Fossen, 2011):
2 2
G G Gm u vr wq x q r y pq r z pr q X
2 2
G G Gm v wp ur y r p z qr p x qp r Y
2 2
G G Gm w uq vp z p q x rp q y rq p Z
2 2
+
x z y xz yz xy
G G
I p I I qr r pq I r q I pr q I
m y w uq vp z v wp ur K
2 2
+
y x z xy zx yz
G G
I q I I rp p qr I p r I qp r I
m z u vr wq x w uq vp M
2 2
+
z y x yz xy zx
G G
I r I I pq q rp I q p I rq p I
m x v wp ur y u vr wq N
(3.10)
Chapter 3. AUV Equations of Motion
35
The forces , ,X Y Z acting on rigid body are defined in the Body-fixed frame, where X is the
force acting along the X axis, Y acts along the Y axis, and Z acts along the Z axis. The mo-
ments , ,K M N acting on the body are defined similarly, where K is the moment acting about
the X axis in a right-hand fashion, M acts about the Y axis, and N acts about the Z axis.
In the matrix form, the equation of motion of an AUV can be rearranged and written as follows:
RB RB RB M υ C υ υ τ (3.11)
where RB
M is the rigid-body inertia matrix, and RBC υ υ represents the Coriolis and centripe-
tal forces due to the vehicle’s motion in a rotating reference frame, RBτ is the vector of external
rigid body force.
Let the vehicle’s inertia tensor 0I and the centre of gravity
Gr be defined as
0
xx xy xz
yx yy yz
zx zy zz
I I I
I I I
I I I
I (3.12)
T
G G G Gx y z r (3.13)
Then the rigid-body inertia matrix RB
M may be defined by 0
, ,Gr I and vehicle m as
3 3
0
0 0 0
0 0 0
0 0 0
0
0
0
G G
G G
G GG
RBG G x xy xzG
G G yx y yz
G G zx zy z
m mz my
m mz mx
m my mxm m
mz my I I Im
mz mx I I I
my mx I I I
I S rM
S r I (3.14)
The rigid body inertia matrix RB
M is constant, positive definite and symmetric.
The Coriolis and centripetal forces RBC υ υ are determined by the inertia matrix
RBM as a
function of velocity .υ Let M be an arbitrary inertia matrix described as:
Chapter 3. AUV Equations of Motion
36
11 12
21 22
M MM
M M (3.15)
Then the Coriolis matrix C υ is defined as:
11 12
11 12 21 22
3×3
RB
0 -S M v +M wC υ
-S M υ+M w -S M v+M w (3.16)
The Coriolis and Centripetal matrix RBC , is presented with an skew-symmetric form as:
0 0 0
0 0 0
0 0 0
0
RBG G G G
G G G G
G G G G
G G G G
G G G G
G G G G
yz xz z yz xy y
yz
m y q z r m y p w m z p v
m x q w m z r x p m z q u
m x r v m y r u m x p y q
m y q z r m x q w m x r v
m y p w m z r x p m y r u
m z p v m z q u m x p y q
I q I p I r I r I p I q
I q
C ν
0
0
xz z xz xy x
yz xy y xz xy x
I p I r I r I q I p
I r I p I q I r I q I p
(3.17)
The next section discusses the vector of external rigid body force .RBτ
3.4.2 External Rigid Body Force
The vector of external rigid body force RBτ consists of the hydrostatic force ,
Sτ hydrodynamic
force ,Hτ and propulsion force .
propτ These external forces are described in the next sections.
RB S H prop τ τ τ τ (3.18)
3.4.2.1 Hydrostatic Force
The hydrostatic force includes the gravitational and buoyant forces, which act on the CG of the
vehicle. The hydrostatic force is defined in the Body Fixed Coordinate as (Feldman, 1979):
Chapter 3. AUV Equations of Motion
37
sin
( )cos sin
( )cos cos
( )cos cos ( )cos sin
( )sin ( )cos cos
( )cos sin ( )sin
S
G B G B
G B G B
G B G B
W B
W B
W B
y W y B z W z B
z W z B x W z B
x W x B y W y B
τ (3.19)
where W mg is the submerged weight of the AUV, B g is the buoyancy, is the fluid
density, is the volume of the AUV hull, , ,B B B
x y z and , ,G G G
x y z are the centre of gravity
and centre of buoyancy respectively.
3.4.2.2 Hydrodynamic Forces
The hydrodynamic forces Hτ are due to pressure exerted on the body by the surrounding fluid
as the vehicle moves and accelerates through the fluid. The hydrodynamic force is decomposed
into terms including added mass, added Coriolis-centripetal and hydrodynamic damping as
follows:
H A Aτ = - M υ+C υ υ D υ υ (3.20)
The added mass and hydrodynamic damping forces are a function of the density of water, the
geometric shape of the vehicle - which is assumed to be a prolate ellipsoid and the vehicle’s
velocity (Fossen, 2011).
Added mass
The accelerated fluid flow around the moving vehicle generates the component, which accounts
for the inertia of the surrounding fluid, termed added mass. The fluid surrounding the vehicle
body is accelerated with the body itself, a force is necessary to achieve this acceleration; the fluid
exerts a reaction force, which is equal in magnitude and opposite in direction. This reaction force
is the added mass contribution (Antonelli, 2013). Added mass effects are modelled as a function
of acceleration. The added matrix of inertia is defined as:
Chapter 3. AUV Equations of Motion
38
u v w p q r
u v w p q r
u v w p q r
A
u v w p q r
u v w p q r
u v w p q r
X X X X X X
Y Y Y Y Y Y
Z Z Z Z Z Z
K K K K K K
M M M M M M
N N N N N N
M (3.21)
The matrix is determined by vehicle external geometry. Each term represents the force generated
in a given direction by an acceleration in a given direction. For example, the force A
Z along the
Z axis due to an acceleration u along the X axis is expressed .A u
Z Z u
In this study, it is assumed that the vehicle has three planes of symmetry and fully submerged
in the water. For a three plane of symmetry AUV, the contribution of the non-diagonal compo-
nents of the added mass matrix could be neglected. Consequently, only the diagonal compo-
nents are taken into account and the added mass matrix is presented as:
, , , , ,u v w p q r
diag X Y Z K M N A
M (3.22)
The added mass coefficients are analytically approximated by using the slender body theory
or strip theory based on the geometry of the rigid body and its symmetry. A detailed discus-
sion on the added mass for the marine vehicles is can be found in (Korotkin, 2008).
Coriolis-centripetal forces from added mass
The Coriolis and centripetal matrix due to the added mass can be written in simplified form as:
0 0 0 0
0 0 0 0
0 0 0 0
0 0
0 0
0 0
w v
w u
v u
w v r q
w u r p
v u q p
Z w Y v
Z w X u
Y v X u
Z w Y v N r M q
Z w X u N r K p
Y v X u M q K p
AC υ (3.23)
Chapter 3. AUV Equations of Motion
39
Hydrodynamic damping forces and moments
The hydrodynamic forces and moments have a dominant effect in the vehicle motion. The hy-
drodynamic damping terms may be grouped into linear and quadratic terms as a common sim-
plification as follows:
l qD υ = D +D υ (3.24)
where
0 0 0 0 0
0 0 0
0 0 0 0
0 0 0
0 0 0 0
0 0 0
u
v p r
w q
v p r
w q
v p r
X
Y Y Y
Z Z
K K K
M M
N N N
lD (3.25)
0 0 0 0 0
0 0 0
0 0 0 0
0 0 0
0 0 0 0
0 0 0 0
u u
v v p p r r
w w q q
v v p p r r
w w q q
v v r r
X u
Y v Y p Y r
Z w Z q
K v K p K r
M w M q
N v N r
qD υ (3.26)
The quadratic damping terms dominate as an underwater vehicle operating in an unbounded
fluid. For the low velocities, the quadratic terms may be considered negligible (Fossen, 2011).
The hydrodynamic damping coefficients are considered constant for the vehicle utilised in this
study. In order to simply the model, it is assumed that the angular coupled terms are neglected
since their values are relatively small. The detailed estimation of these coefficients is beyond the
scope of this work.
Chapter 3. AUV Equations of Motion
40
3.4.2.3 Control Surfaces Forces
A torpedo shaped underwater vehicle is usually equipped with two different control surface
arrangements, namely the cruciform configuration and the X-form configuration. Figure 3.3
shows the two control surface configurations viewed from astern, the cruciform in the left and
the X-form in the right. In the cruciform configuration, the vertical rudders and horizontal ele-
vators are controlled independently. On the other hand, for the X-form configuration, all four
rudders rotate simultaneously to perform a specific manoeuvre.
Figure 3.3. Two types of the control surface configuration.
In case of the X –form configuration, the effective (movable) area is greater with respect to the
cruciform configuration (all 4 rudders are deflected) and, consequently, a larger manoeuvring
(destabilizing) lateral force is exerted to the submarine (Dubbioso et al., 2017). The X-form con-
figuration shares most of the properties of the cruciform configuration, but it has mixed control
surface control providing maximum moment in pitch, and yaw manoeuvres.
The Gavia AUV is propelled and manoeuvred with a three-bladed propeller and four independ-
ent control surfaces in X-form configuration located aft of the propeller as shown in Figure 3.4.
The control surfaces can be commanded separately by independent servomotors and are em-
Chapter 3. AUV Equations of Motion
41
ployed simultaneously to generate accurate and fast moments. The whole unit is protected in-
side a Nautican type nozzle. This propulsion configuration is unique to Teledyne Gavia that
provides high efficiency in both low-speed and high-speed manoeuvers.
Figure 3.4. Gavia Propulsion system.
Assuming that the cross-configuration has a mounting of 45 degrees from the AUV vertical line,
the hydroplane force for one blade for each configuration will be:
*
2
y
y
FF
(3.27)
where y
F
is the force of one blade in the cruciform configuration.
The forces and moments created by the actuators are directly proportional to the angle of de-
flection and to the square of the AUV forward speed. Forces and moments due to control surface
deflection can be approximated by a second order polynomial function if the deflection angle is
small enough that the flow over the control surface does not stall.
3.4.3 Determination of the Hydrodynamic Coefficients
A Gavia class modular, torpedo-shaped AUV was used as the platform this study. The vehicle
in its tested configuration consisted of a Nose Cone Module, Battery Module, Acoustic Doppler
Current Profiler module, Inertial Navigation System module, Control Module and a Propulsion
module. There are some transducers equipped with AUV such as the obstacle avoidance sonar,
Chapter 3. AUV Equations of Motion
42
acoustic modem transducer, and side scan sonar. The overall length of the vehicle was 2.7 m and
a maximum hull diameter of 0.2 m and the dry weight in air was approximately 70 kg.
Techniques for estimating the hydrodynamic coefficients of fully submerged vehicles can be
traced back to the tools originally developed to predict the aerodynamic coefficients of airships
and subsequently adopted for submarines (De Barros et al., 2008). There are generally four main
approaches to estimate the hydrodynamic coefficients of an underwater vehicle, including the
CFD method, analytical method, experimental approach using model test in towing tank, and
the system identification (SI) approach using real system test. In this thesis, the analytical
method and the SI approach are utilised. The analytical method is applied to estimate the coef-
ficients in the non-linear model used for the simulation study. The SI approach is employed for
the control design that is discussed thoroughly in chapter 7.
The nonlinear hydrodynamic coefficients in this chapter are estimated using the Prestero ap-
proach and Fossen model as illustrated in (Prestero, 2001b) and (Fossen, 2011).
The added mass in the x-axis is derived by approximating the hull of the vehicle by an ellipsoid
with a minor axis is haft of the vehicle diameter and a major axis is haft of the vehicle length
(Blevins, 1979):
24
3 2u
lX r
(3.28)
where is empirically determined by the ratio of the vehicle to the diameter.
For the calculation of crossflow and roll added mass, the strip theory is applied. In the strip
theory, the crossflow and roll added mass is approximated as a sum of slices along the body.
These added mass coefficients are calculated using integrals along the x-axis as shown in the
following equations:
Chapter 3. AUV Equations of Motion
43
v w a
x
Y Z m x dx (3.29)
w v r q a
x
M N Y Z xm x dx (3.30)
2
q r a
x
M N x m x dx (3.31)
42
f
p
x
K a dx
(3.32)
where a
m represents the added mass per length unit and is defined as:
2
422
2
for cylinder
( ) for the cylinder with fin
a
f
f
R x
m x R xa R x
a
(3.33)
a is the length of fin taken from the central axis
f
x is the sector along the x-axis where the fins are located.
The nonlinear axial drag coefficients is calculated as
1
2 D fu uX C A (3.34)
where D
C is an empiric coefficient.
fA is the vehicle frontal area.
The nonlinear crossflow drag is considered to the summation of the vehicle hull and fin cross-
flow drag. It is calculated due to the symmetry of vehicle using integrals from the strip theory
as:
Chapter 3. AUV Equations of Motion
44
2 2v v w w
x
Y Z R x dx (3.35)
2 2finw w v v
x
M N xR x dx x (3.36)
2 2fin finr r q q
x
Y Z x x R x dx x x (3.37)
3 32 2finq q r r
x
M N x x R x dx x (3.38)
where 1
2 dcc
1
2 fin dfS c
dc
c is the crossflow drag coefficient of a cylinder.
df
c is the damping crossflow coefficient.
The crossflow drag coefficient dc
c is estimated taking the empirical values.
The damping crossflow coefficient dfc can be expressed using the following equations:
0.1 0.7df
c t (3.39)
where t is the ration of the widths of the top and bottom of the fin along the vehicle x-axis.
The developed coefficients were non-dimensionalised with the length of the vehicle. A number
of studies on the hydrodynamic coefficient estimation of Gavia AUV have been conducted in
the literature. The hydrodynamic coefficients are verified by comparing with similar works re-
ported in the literature (Porgilsson, 2006) (Helgason, 2012) and with the data provided by the
manufacturers.
Chapter 3. AUV Equations of Motion
45
3.5 Summary
A complete mathematical model for an autonomous underwater vehicle was discussed in chap-
ter 3. This chapter covered the system of equations used for the experiments and simulations
described in subsequent chapters. The modelling of an AUV involved the development of both
kinematic and dynamic model. The analytical and theoretical method to estimate the hydrody-
namic coefficients were briefly presented. The hydrodynamic coefficients were then incorpo-
rated into the equations of motion to obtain the complete mathematical model of an AUV.
46
CHAPTER 4
Experimental Study of the Conventional
Fixed Pitch Propeller
This chapter presents the open water propeller characteristics and the four-quadrant propeller
models as applied to a torpedo shaped underwater vehicle. A series of experiments with a Gavia
AUV propeller were conducted in the towing tank using a rotor testing apparatus. The purpose
of these tests was to measure the propeller thrust and torque under varying flow conditions to
then be used as the basis of the developed propeller models. These mathematical models were
constructed using two regression models, a polynomial and a Fourier series. Model coefficients
were derived using the method of least squares and a comparison analysis was also conducted
to test the robustness of the methodology. Results show that the Fourier series models are able
to produce a reasonable and accurate approximation of thrust and torque coefficients with a
small number of parameters in the examined condition of this study. The obtained four-quad-
rant open water characteristics of the AUV propeller model were utilised to improve the system
mathematical model for more accurate simulation and controller design, to compare the AUV
performance equipped with CCPP propulsion system.
47
Part of this chapter has been published in the “Proceedings of the Institution of Mechanical Engineers,
Part M: Journal of Engineering for the Maritime Environment”. The citation for the journal paper is:
Tran M, Binns J, Chai S, et al. (2017). A practical approach to the dynamic modelling of an un-
derwater vehicle propeller in all four quadrants of operation. Proceedings of the Institution of Me-
chanical Engineers, Part M: Journal of Engineering for the Maritime Environment.
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
48
4.1 Introduction
There have been significant attempts to determine the performance of marine propellers in the
literature by applying analytical approximations, experimental fluid dynamics (EFD), and com-
putational fluid dynamics (CFD). A simplified model operating in the first quadrant is com-
monly utilised and, in several cases, the detailed modelling in all the four quadrants of operation
is necessary. For ships and vessels in conventional operation, obtaining accurate thrust and
torque values for positive shaft speed and advance speed are commonly investigated and mod-
elled (Carlton, 2012). For underwater vehicles such as AUVs, it is important to model propeller
thrust and torque in all four quadrants since the four-quadrant propeller model is able to cover
a full range of operation which include a complete representation of propeller thrust and torque
for both directions of propeller and fluid velocity (Brown, 1993). By applying the four-quadrant
propeller model in the vehicle simulation and control model, the performance prediction in the
conditions such as braking, stopping and running astern would be obtainable. Another im-
portant advantage of the four-quadrant model is that it provides a continuous function to esti-
mate the thrust and torque applied in the simulation and control design. The four quadrants of
operation are defined and summarised in Table 4.1 with the ( ) and ( ) signs represented for
the positive and negative direction accordingly.
Table 4.1. Definition of four quadrants
Quadrant Vehicle Speed A
V Propeller Speed n Advance angle
st1 0 90
nd2 90 180
rd3 180 270
th4 270 360
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
49
Some of early studies on four-quadrant models have been discussed for the well-known Wa-
geningen propeller B-series (Van Lammeren et al., 1969; Kuiper, 1992; Oosurveld and Van
Oossanen, 1975; Oosterveld, 1970) and recently for the C and D-series (Dang et al., 2012) devel-
oped by the Maritime Research Institute Netherlands. These fixed pitch propeller (FPP) and
controllable pitch propeller (CPP) series comprise the propeller characteristics primarily de-
signed for the merchant ships (Dang et al., 2012). The four-quadrant mathematical models of the
propeller derived from the Wageningen B-series were implemented in the ship manoeuvring
simulation systems in (Sutulo et al., 2002; Khaled and Chalhoub, 2011; Tannuri et al., 2014;
Woodward et al., 2005; Delefortrie and Vantorre, 2009). The method to experimentally deter-
mine the four-quadrant model for marine thruster employ thin aerofoil theory and experimental
data (Bachmayer et al., 2000). However, the proposed model was intentionally applied for the
low-speed and hovering manoeuvrability of an underwater vehicle since it was derived with
the assumption of zero advance velocity, the “Bollard-pull” condition. This was taken further to
a nonlinear model for the axial flow velocity through the propeller blade and included a propel-
ler model to reproduce the thrust over the four-quadrant range (Pivano et al., 2006). The feed
forward neural networks (FFNN) was utilised to train a neural network using the data obtained
from previous four-quadrant tests of the Wageningen propeller B-series (Roddy et al., 2007).
This method provides a means for estimating the four-quadrant model of the propellers in the
series for which the measured data is not available.
Although there is a wealth of information on the propeller modelling, the published data in the
literature did not provide sufficient information to reproduce the propeller performance char-
acteristics in four quadrants, especially for the investigation of underwater vehicle manoeuvra-
bility. The available data is exclusively applied to ship and vessel propeller in the first quadrant.
In addition, the approach to derive the approximation functions representing the experimental
results for the four quadrant measurements have not been thoroughly examined.
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
50
This chapter presents an experimental study on the propeller of the Gavia AUV, a vehicle man-
ufactured by Hafmynd ehf and currently in service at the Australian Maritime College. Results
are presented from two different regression models, polynomial and Fourier series, to describe
experimental data for a four-quadrant propeller model. The model coefficients of these two
models are derived by using the curve fitting technique - Least Squares method.
4.2 Propeller Dynamic Modelling
Modelling the thrust and torque produced by a propeller is a complicated task, since it is diffi-
cult to develop a finite-dimensional analytical model from the laws of physics (Pivano et al.,
2009). A combination of simplified analytical and empirical models is therefore the commonly
utilised since it is reliable and computational efficient. This approach utilises the analysed ex-
perimental data combined with the empirical equations to estimate the fundamental propeller
characteristics. From the simulation and control point of view, the models are required to be
identified accurately to capture the primary hydrodynamic performance. If the models were too
complicated, the controller designed would be of high order with weak robustness and low re-
liability. As a result, the system would experience unstable conditions. The relevant practical
method is the estimation of thrust and torque using the empirical equations that relate the non-
dimensional coefficients. In this chapter, the fully submerged underwater vehicle propeller is
considered so that the unsteady flow effects such as air suction, cavitation, Wagner’s effect, and
Kuessner effect can be neglected (Fossen and Blanke, 2000). The following models are therefore
presented based on quasi-steady thrust and torque modelling.
4.2.1 The Propeller Open Water Characteristics Curves
The propeller open water characteristics curves refer to the first quadrant performance of the
four-quadrant operation in uniform flow conditions. The results of open water tests of propeller
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
51
are presented in the form of non-dimensional coefficients of speed, thrust and torque. The ad-
vance ratio J , the thrust coefficient T
K and the torque coefficient Q
K are defined as:
AV
JnD
(4.1)
2 4T
TK
n D (4.2)
2 5Q
QK
n D (4.3)
where the propeller thrust T and torque Q are characterized by the dimensionless open water
coefficients ( )T
K J and ( )Q
K J , respectively, where J is the advance ratio and n (RPS) is the
propeller rotational speed, D (m) is the propeller diameter, A
V (m/s) is the vehicle advance
speed, and 3(kg/m ) is the water density.
The values of the non-dimensional thrust coefficient T
K and torque coefficient Q
K calculated
from experimental data are approximated with sufficient accuracy using nonlinear polynomial
regression analysis. They are defined as the function of advance ratio J in the form:
0
( )k
x
T xx
K J m J
(4.4)
0
( )k
x
Q xx
K J n J
(4.5)
where the polynomial coefficients x
m and x
n are determined by using the least-squares curve
fitting technique.
The T
K and Q
K versus J characteristic curves contain all of the information necessary to define
the propeller performance at a particular design operating condition (Carlton, 2012). For the
testing of a propeller series, the Wageningen B-series for example, the results of T
K and Q
K
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
52
values could be presented systematically as the polynomial functions of J and other propeller
geometric parameters such as the number of blades ( )Z , the pitch to diameter ratio ( / )P D ,
blade area ratio ( / )E O
A A and Reynolds number n
R (Carlton, 2012; Van Lammeren et al., 1969;
Oosurveld and Van Oossanen, 1975; Kuiper, 1992):
( , , / , / , )T E O n
K f J Z P D A A R (4.6)
( , , / , / , )Q E O n
K g J Z P D A A R (4.7)
The open water efficiency is defined as the ratio of the thrust horsepower to delivered horse-
power (Carlton, 2012):
THP
DHP 2 2a T
O
Q
TV K J
nQ K
(4.8)
The models based on these coefficients are only applicable in the regime of non-zero propeller
velocities, where the rotational direction must be the one that drives the vehicle forward. This is
the conventional way of operating a propeller, but for studying manoeuvring situations or
astern performance of vehicle other data is required (Carlton, 2012). A zero-crossing of the pro-
peller speed in such conditions would make the advance ratio go to infinity.
4.2.2 The Propeller Four-quadrant Mathematical Model
Despite being available for decades, four-quadrant propeller models are not widely used in the
marine simulation and control study. In the case of the fixed pitch propeller it is possible to
define four-quadrant propeller characteristics model which is based on the advance angle of
the propeller blade at radius 0.7R :
arctan arctan arctan0.7 0.7 0.7
A AV VJ
nD R
(4.9)
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
53
where 2
DR is the propeller radius, and 2 n is the propeller angular velocity.
For multi-quadrant studies, the advance angle notation offers a considerably more flexible
representation than the conventional advance coefficient ,J for example when propeller speed
approaches zero, the advance coefficient 0,J thrust and torque coefficients
TK and
QK all ap-
proach infinity and have a discontinuity. This formulation has many advantages over the open-
water characteristics, since it is based on a physical foundation: it is valid for any shaft speed
and inflow, and covers all four quadrants of operation.
4.2.3 Four-quadrant Model Representations
Provided sufficient experimental data is available it becomes possible to define the thrust and
torque characteristics of the propeller in each quadrant (Carlton, 2012). To determine the per-
formance characteristics at other quadrants other than the first quadrant the open water dia-
grams has to be expanded. The four-quadrant propeller characteristic is usually presented using
the non-dimensional thrust and torque coefficients T
C and Q
C as functions of .T
C and Q
C
are computed as follows (Carlton, 2012; Kuiper, 1992):
2222 2
8
1 0.70.72 4
TT
A
KTC
JV R D
(4.10)
2222 3
8
1 0.70.72 4
Q
Q
A
KQC
JV R D
(4.11)
The propeller characteristic curves are periodic over the range 00 360 and can be deter-
mined by experiment and smoothly interpolated in four quadrants by using the nonlinear pol-
ynomial and the Fourier series approximation.
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
54
0
( )k
x
T xx
C m
(4.12)
0
( )k
x
Q xx
C n
(4.13)
00
( ) cos sini
T k kk
C m m k n k
(4.14)
00
( ) cos sini
Q k kk
C m m k n k
(4.15)
where is the frequency of the signal,
i is the number of terms,
xm ,
km ,
xn ,
kn are the function coefficients determined by applying the method of LS.
Similar to the coefficient representation in the first quadrant, the non-dimensional coefficients
of a propeller series cover four quadrants operation could be expressed systematically as the
functions of a range of number of blades ( ),Z the pitch to diameter ratio ( / ),P D blade area ratio
( / )E O
A A and Reynolds number .n
R
( , , / , / , )T E O n
C f Z P D A A R (4.16)
( , , / , / , )Q E O n
C g Z P D A A R (4.17)
For an effective computation in the simulator, a simplified four-quadrant model is obtained by
utilising fewer terms associated with sines and cosines functions in the expansion of T
C and Q
C .
In (Smogeli, 2006), the authors derived the model by applying only the first terms:
0 1 1( ) cos sin
T T T TC m m n (4.18)
0 1 1( ) cos sin
Q Q Q QC m m n (4.19)
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
55
4.2.4 The Least Squares Fitting Method
The curve fitting techniques or regression methods use the provided series of experimental data
to estimate the coefficients of an empirical parametric model. The coefficients are estimated by
applying the least squares method, which minimises the sum square of residual or the differ-
ence between the measured data and the fitted data.
Let y denote the empirical function to be determined and can be written in the form of equation
(4.20):
( , )y f x (4.20)
where x is the input data and is the vector of model coefficients.
The measured data i
y of i
y in the experiment is defined as:
*
i i iy y (4.21)
where i is the estimation error.
The identification of coefficient is equivalent to the minimization of a scalar cost function
21 1( ) ( ( , ))
2 2i i iJ y f x (4.22)
Solving equation 0J
for the unknown parameter gives the estimation of . The compre-
hensive solutions to this equation are described in relevant reference (Van Der Heijden et al.,
2005; Klein and Morelli, 2006).
In this study, the polynomial functions and the Fourier series expressed in equations (4.12-4.15)
are the empirical functions to be examined for representing the experimental data.
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
56
4.3 Experimental Study
The objectives of the tests were to derive a set of Gavia AUV propeller thrust and torque data
under the four-quadrant conditions. A three-bladed Gavia AUV FPP, as shown in Figure 4.1,
was selected for the tests. This propeller is made from aluminium alloy and particularly de-
signed for the torpedo shaped underwater vehicle. An adapter was specifically designed and
manufactured to fit the propeller into the driving shaft of the testing apparatus as shown in
Figure 4.2. The fundamental specifications of the tested Gavia propeller are also listed in Table
4.2 below.
Figure 4.1. Gavia AUV propeller.
Figure 4.2. Propeller attached into an adaptor.
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
57
Table 4.2. Fundamental specifications of tested propeller.
Symbol Description Value Unit
Scale 1:1
Z Number of blades 3
D Diameter 0.143 m
/P D Pitch ratio 1.7
/E O
A A Blade area ratio 0.4
OA Disk area 0.0161 2m
4.3.1 Open Water Test Setup
The open water tests are usually performed in the towing tank. The experiments in this study
were conducted in the towing tank at AMC as shown in Figure 4.3. The primary dimensions of
the AMC towing tank are listed in Table 4.3.
Table 4.3. Towing tank dimensions.
Length Width Depth Maximum speed
100 m 3.55 m 0 to 1.5 m 0 to 4.6 m/s
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
58
Figure 4.3. The towing tank at AMC-UTAS.
The key equipment for the open water tests was the propeller open water dynamometer, shown
in Figure 4.4. Further details of the propeller open water dynamometer can be found in (Liu et
al., 2015; Liu et al., 2014), which was designed and built during the that project.
Figure 4.4. Propeller Open Water Dynamometer.
The thrust and torque of propeller were measured by a Cussons Propulsion Dynamometer R31.
This R31 dynamometer was mounted in line with the shaft of the propeller, and the dynamom-
eter static calibration was carried out before the test. The driving motor was the Dunkermotoren
BG 75 attached behind the dynamometer. An encoder was used to measure propeller rotational
speed (RPM) and the motor speed was controlled from the computer on the carriage by the
encoder feedback signal. Both the dynamometer and the driven motor were located inside the
Propeller Open Water Dynamometer as shown in Figure 4.5.
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
59
Figure 4.5. Internal assembly of Propeller Open Water Dynamometer.
4.3.2 Data Acquisition and Post Processing
The measured data were acquired with the National Instruments BNC-2090 acquisition system
and a LabVIEW software program was developed to ensure accurate data acquisition. The in-
house developed program was able to control the propeller rotational speed at desired constant
values and acquire the measured data via different channels. A sampling rate of 1000 Hz was
selected with sampling time was 20s for the acquired signals. The low pass Kalman filter was
also applied in order to reduce the high frequency noise of collected raw data. A schematic dia-
gram and a photo of the experimental setup and data acquisition system are given in Figure 4.6.
Figure 4.6. The experimental setup of Propeller Open Water Test.
The four-quadrant tests were conducted by varying the carriage speed and direction, the pro-
peller rotational speed and the direction of rotating propeller. The experiments were run at a
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
60
wide range of advance ratio, especially at off design conditions on both ends of the range in
order to evaluate the performance characteristics of the AUV equipped with this propeller dur-
ing manoeuvring. In a conventional open water propeller test, for each quadrant condition, the
propeller rotational speed is kept constant while the advance speed of the propeller varies, as
recommended by procedures and guidelines of the International Towing Tank Conference
(ITTC) (ITTC, 2008a). The carriage speed was set at different constant speed in the range from
0.5 m/s to 3 m/s during these tests. The tests with negative advance speed were conducted
with reversely mounted propeller without changing motion direction of the carriage to avoid
effect of the submerged testing apparatus on the propeller. From equation (4.9), the relationship
between and J over the four quadrants is intensively described in Table 4.4 below:
Table 4.4. The relationship between and J in the four quadrants.
First quadrant Second quadrant
0 26 69 90 95 112 146 180
J 0 1.1 5.7 -28 -5.5 -1.5 0
Third quadrant Forth quadrant
190 206 241 270 275 300 327 360
J 0.4 1.1 3.9 -25 -3.7 -1.5 0
It can be seen from Table 4.4 that to cover the full range of in each quadrant, the advance ratio
J had to be adjusted progressively from 0 to very high values in the tests. This procedure was
difficult to manage in practice due to the physical limitations of the facility. In addition, the high
values of J refer to the off-design conditions in which the underwater vehicles would not ma-
noeuvre in practical application as they are not realistic. Therefore in the presented tests, within
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
61
the capability of models and instrumentations, the advance ratio J was controlled up to 1.5 in
the first and third quadrant and to -1.5 in the second and forth quadrant. It should be noted that
when 0 and 360 , or 0J the model was at the bollard pull conditions. Moreover, for
the condition when 90 and 0270 the propeller was stationary and the loads were ob-
tained by dragging the propeller through the water without rotating in both forward and back-
ward directions. The measured data at these cases are important in the estimation of the curve
fitting functions.
4.3 Results and Discussions
4.3.1 Open Water Performance Results
The first quadrant performance or the open water characteristic curve of the Gavia AUV propel-
ler is presented in this section. The propeller model in the first quadrant is initially discussed
since it is the most important phase in which the underwater vehicles are primarily designed to
operate.
The collected raw data was processed and characterised in the regression analysis. For most
propellers, the open water characteristic curves can be approximated with sufficient accuracy
by a second-degree polynomial:
2( ) 0.1436 0.1633 0.2860T
K J J J (4.23)
210 ( ) 0.3095 0.0572 0.4004Q
K J J J (4.24)
The presented curves are drawn based on the second order polynomials and is given in Figure
4.7. In this diagram, the non-dimensional open water thrust coefficient ,T
K torque coefficient
QK and the efficiency
0 are plotted against the advance ratio .J
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
62
Figure 4.7. Gavia AUV propeller open water diagram.
The largest values of T
K and 10Q
K are 0.28 and 0.4, respectively at 0,J the condition in
which the propeller is rotating without translating. The maximum efficiency is 62% at 0.8J .
Some minor oscillations occur at the high J value due to the system mechanical vibration. The
experimental measurements were filtered and analysed based on the mechanical vibration fre-
quency measured by a separated accelerometer attached on the system.
4.3.1 Four-quadrant Models Results
4.3.1.1 Polynomial Regression Models
The thrust coefficient T
C and torque coefficient Q
C for the Gavia AUV propeller in the range of
advance angle from 0 to 360 are described by the nonlinear polynomial regression models
with the degree from 2 to 9 as shown in Figure 4.8 and Figure 4.9.
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
63
Figure 4.8. Comparison of different polynomial regression models with measured experi-
mental data for torque coefficient T
C .
Figure 4.9. Comparison of different polynomial regression models with measured experi-
mental data for thrust coefficient Q
C .
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
64
As was mentioned in the previous section, the measured data in the entire range of could not
be practically obtained. Therefore, the experimental data were allocated in specific regions on
the graphs where the testing conditions were feasible. It is seen from Figure 4.8 that the polyno-
mial models for T
C represent the data really well at high degrees, such as the sixth and seventh
order polynomial. However, for the polynomials with the order higher than seven, the over-
fittings occur at 90 and 270 . In the same manner, the polynomial up to seventh order
appears to be adequate for describing the Q
C data as demonstrated in Figure 4.9. The low order
polynomials are not able to fit the data in the range of from 150 to 0220 . The over-fittings
are resulted from the high order polynomials and the curve characteristics are varied that is not
able to present the nature of the propeller performance.
After fitting the data by using polynomial regression models with different orders, the applica-
bility of fit is assessed to evaluate the validity. There are three statistic criteria to be considered:
the Sum of Squares due to Error SSE , the Root Mean Squared Error RMSE , and coefficient of
determination 2R . The SSE calculates the total deviation of the output values from the fitted
curve to the output values and the RMSE is an estimation of the standard deviation of the ran-
dom value in the data. These values closer to 0 show that the obtained model is more useful and
effective for prediction. Coefficient of determination 2R indicates the proportionate of variation
in the output variables explained by the input variables in the regression model. The values of
2R close to 1 demonstrate that the regression models are appropriate for extrapolation. The sta-
tistic criteria ,SSE ,RMSE and 2R for the T
C and Q
C coefficients are calculated and listed in the
Table 4.5.
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
65
Table 4.5. Statistical properties for polynomial regression.
Thrust coefficient T
C Torque coefficient Q
C
Number
of Orders SSE RMSE 2R SSE RMSE 2R
2 0.1213 0.0402 0.8178 0.0026 0.0058 0.9147
3 0.0168 0.0151 0.9748 0.0003 0.0022 0.9883
4 0.0132 0.0134 0.9802 0.0004 0.0025 0.9851
5 0.0069 0.0098 0.9896 0.0004 0.0025 0.9866
6 0.0059 0.0091 0.9911 0.0004 0.0025 0.9862
7 0.0057 0.0090 0.9914 0.0002 0.0018 0.9923
8 0.0040 0.0076 0.9940 0.0001 0.0015 0.9952
9 0.0038 0.0075 0.9943 0.0001 0.0015 0.9956
It can be seen in Table 4.5 that the ninth order polynomial has the least SSE and RMSE values
for both T
C and Q
C coefficients. In addition, its coefficient of determination 2R is highest and
close to 1 compared to others. However, as previously discussed the polynomials with the order
higher than seven overfit the data for both T
C and Q
C coefficients. Increasing the number of or-
der in the polynomial would give better the applicability of fit but cause the over-fitting. For the
polynomials with the order from two to seven, the seventh order polynomial has the least SSE
and RMSE values, and highest 2R value. Therefore, the seventh order polynomial is consid-
ered the finest polynomial model in the examined condition.
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
66
4.3.1.2 Fourier Series Regression Models
The Fourier series regression models with the number of terms from one to six are applied to
represent the thrust coefficient T
C and torque coefficient Q
C for the propeller in the range of
advance angle from 0 to 360 . The comparison of different Fourier series regression models
with measured experimental data for T
C and Q
C are shown in Figure 4.10 and Figure 4.11. It
can be seen in Figure 4.10 that the four-term and five-term Fourier series provide the better fit
to the experimental data than the lower term models for T
C . For the Fourier series with the
number of term higher than five, the over-fittings occur as seen in the range of from 45 to
135 and from 270 to 315 . It is also observed from Figure 4.11 that three-term Fourier series
provide the better fit to the experimental data compared to other models for the values of Q
C .
As the number of term increases the curves reach unreasonably high values, which is considered
as over-fitting. Additionally, the nature of these curve forms are incorrectly changed.
Figure 4.10. Comparison of different Fourier series regression models with measured experi-
mental data for thrust coefficient T
C .
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
67
Figure 4.11. Comparison of different Fourier series regression models with measured experi-
mental data for torque coefficient Q
C .
Table 4.6. Statistical properties for Fourier series regression.
Thrust coefficient T
C Torque coefficient Q
C
Number
or Terms SSE RMSE 2R SSE RMSE 2R
1 0.0270 0.0191 0.9595 0.0005 0.0027 0.9797
2 0.0071 0.0099 0.9893 0.0003 0.0020 0.9887
3 0.0045 0.0080 0.9932 0.00003 0.00066 0.9989
4 0.0036 0.0072 0.9947 0.00001 0.00049 0.9994
5 0.0037 0.0074 0.9945 0.00001 0.00049 0.9994
6 0.0024 0.0061 0.9964 0.00001 0.00045 0.9995
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
68
Three similar statistic criteria used above are also be considered for evaluating Fourier series
regression models: ,SSE RMSE , and 2R . They are calculated and listed in Table 4.6.
It can be seen in Table 4.6 that the SSE and RMSE values decrease and 2R value increases in
general as the number of terms increase for both T
C and Q
C coefficients. This fact illustrates
that increasing the number of terms could make the resulting curves fit with the experimental
data better. However, it is noted previously that the Fourier series models with the number of
term higher than five overfit the thrust coefficient Q
C and the models with the number of term
higher than three overfit the torque coefficient .Q
C In addition, considering the four-term and
five-term Fourier series model for T
C coefficient they are almost identical as can be seen in Table
4.6. Nevertheless, there is a difference in their statistical properties, which show that the four-
term Fourier series model provides a better fitting curve. It has lower values of SSE and RMSE ,
and higher 2R value compared to the five-term Fourier series model . Therefore, the four-term
Fourier series and the three-term Fourier series models are considered the most suitable Fourier
models for the thrust coefficient T
C and the torque coefficient ,Q
C respectively, in the examined
condition of this study.
4.3.1.3 Results Comparisons
Based on the information and calculations in previous sections, the comparison between the
polynomial and Fourier series model in describing the four-quadrant propeller model is pre-
sented. For the thrust coefficient ,T
C the seventh order polynomial model and the four-term
Fourier series model are compared based on the applicability of fit shown in Table 4.5 and Table
4.6. Although both models are able to produce acceptable approximation of T
C as seen on the
graphs, it can be noted that the statistical results for the thrust coefficient T
C in the four-term
Fourier series model are better than the seventh order polynomial model. The Fourier model
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
69
has lower values of SSE and ,RMSE and higher value considering the 2R compared to the pol-
ynomial model. For the torque coefficient ,Q
C the comparison between the seventh order poly-
nomial model and the three-term Fourier series model is performed based on the statistical val-
ues. It can also be noted that the Fourier model has significantly lower values of SSE and
RMSE compared to those of the polynomial model. In addition, the Fourier model has higher
value considering the 2R as well. It is derived from the examination that the Fourier series
model gives the results to a better agreement for all three statistic criteria: lower SSE , RMSE
value and higher 2R value. It is therefore concluded that the four-term Fourier series and three-
term Fourier series regression models are considered the most appropriate models in represent-
ing the T
C and Q
C coefficients respectively in the specified condition of this study. The model
coefficients from equation (4.14) and (4.15) are calculated and listed in Table 4.7.
Table 4.7. The Fourier series regression function coefficients.
Coefficients 0m
1m
1n
2m
2n
TC 0.0432 -0.0967 0.1455 0.0325 0.0344
QC -0.0055 -0.0152 0.0493 0.0066 0.0020
3m
3n
4m
4n
TC -0.0394 -0.0385 -0.0151 0.0193 1.7390
QC -0.0063 -0.0120 2.0540
Chapter 4. Experimental Study of the conventional Fixed Pitch Propeller
70
4.4 Summary
The experiment of an underwater vehicle propeller was tested at the towing tank in all four
quadrants of operation. The conventional open water performance in the first quadrant and the
performance characteristic in four-quadrant operation were presented in this chapter. An anal-
ysis of using polynomial and Fourier series regression model in representing the experimental
data sets was examined. The applicability of fit was assessed to compare and evaluate the valid-
ity of the proposed models. It was concluded that the four-term and three-term Fourier series
regression models were considered the most appropriate models in representing the thrust and
torque coefficient curves respectively in the specified condition of this study. These two models
formed the four-quadrant underwater propeller model. They were able to produce a reasonable
approximation of thrust and torque coefficients with a small number of parameters.
71
CHAPTER 5
Experimental Study of the Collective and
Cyclic Pitch Propeller CCPP
A series of experimental studies of the innovative propulsor named Collective and Cyclic Pitch
Propeller (CCPP) applied to an underwater vehicle are presented in chapter 5. The bollard pull
and captive model tests were conducted to investigate the characteristics of CCPP and to exam-
ine the effect of different parameter settings to its performance. The obtained results in the form
of force coefficients provide a useful empirical model for the simulation and control of an un-
derwater vehicle equipped with this propulsor.
Part of this chapter has been accepted for publication in the “Journal of Marine Science and Appli-
cation”. The citation for the journal is:
Minh Tran, Hung Nguyen, Jonathan Binns, Shuhong Chai and Alex Forrest, Experimental Study
of the Collective and Cyclic Pitch Propeller, The Journal of Marine Science and Application.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
72
5.1 Introduction
Although the innovative features of CCPP for an underwater vehicle were discovered from pre-
vious research studies its performance characteristics have not been fully demonstrated yet. In
response to the shortcomings of previous works, the experimental studies with underwater ve-
hicle model equipped with the CCPP propulsion system have been conducted at the AMC tow-
ing tank.
In this chapter, the thrust and manoeuvring forces of the CCPP are experimentally investigated
by conducting a series of model tests, including bollard pull test, captive model test, and re-
sistance test. In the bollard pull tests, the CCPP was tested in the stationary condition with dif-
ferent rotational speeds and pitch angle settings. These tests are important to evaluate the CCPP
capability in the operational conditions of no advance speed and at low speed. In the captive
model tests, the CCPP experiments were carried out in the behind hull condition with a series
of different advance coefficients and pitch angle settings to primarily examine its propulsive
performance whilst cruising. In addition, the resistance tests were also conducted and would be
presented in the future study to enable the assessment of the propulsor and model hull interac-
tion.
The main objectives of the present experimental study is to evaluate the characteristics of CCPP
thrust and manoeuvring forces for a range of rotational speed, advance coefficients and pitch
angle settings. The knowledge of these forces is necessary to gain the better understanding of
the innovative design of CCPP and for the optimisation of CCPP system. Moreover, with an
extensive measurement data obtained from the experiments, empirical propulsion model would
be constructed and embedded into the AUV mathematical model to precisely simulate its ma-
noeuvrability.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
73
5.2 Experimental Design
5.2.1 Experimental setup
The experiments in this study were conducted at the AMC towing tank at the University of
Tasmania. The primary specification of the towing tank was described in the previous chapter.
The main components of the testing apparatus including the underwater vehicle model, power
system, transducers, data acquisition system and control system were attached on the towing
carriage. The towing carriage was moved forward and backward with specific speed by the
built-in speed controller.
The underwater vehicle model was mounted from a pair of aluminium vertical struts attached
to the external force balance fixed at the centre of the towing carriage. The height of the struts
were adjusted such that the whole vehicle was immersed 0.9 m below the water surface. Since
the ratio of the tank width to the model transverse dimension is less than 5:1 the tank walls could
be considered not to have significant effect on the propeller force measurements in this experi-
ment (Chakrabarti, 1994).
The entire experimental apparatus is shown in Figure 5.1.
Figure 5.1. The experimental apparatus.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
74
Figure 5.2. The Experimental setup in the Towing Tank.
5.2.2 Force and moment measurements
The experiments were conducted using two types of force balance, an internal force balance and
an external force transducer. The internal balance was a six DOF load cell manufactured by JR3
Multi-Axis Load Cell Technologies. The balance was placed inside a waterproof block and in-
serted behind the propulsion unit. This arrangement enabled the direct measurements of force
and moment generated by the CCPP during the tests. The wires from the load cell were covered
by a watertight seal and connected to the data acquisition system on the towing carriage. The
internal force transducer had the capability of measuring up to 400 N of axial force and 200 N
of side forces.
The external balance was a force transducer designed and manufactured at AMC. It was
mounted at the centre of the towing carriage. This force balance of six single axis load cells was
placed at specific positions enabling the measurement of force and moment experienced by the
entire underwater vehicle model in the six DOF. Each load cell had the measurement capacity
of 225 kg. Figure 5.3 shows the internal and external force transducers used in the experiment.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
75
Figure 5.3. The internal and external force balances.
The balance axis system is given in Table 5.1.
Table 5.1. The force balance axis system.
Balance Axis System Description Positive Direction
X Axial Force or Thrust Forward
Y Horizontal Force To starboard
Z Vertical Force Up
K Rolling moment Roll to starboard
M Pitching moment Turn up
N Yawing moment Turn to starboard
The calibration process was conducted prior to the experiment. A test stand was specifically
designed for the internal force transducer calibration as shown in Figure 5.4. Two force trans-
ducers were carefully calibrated separately. The known loads from 1 kg to 10 kg were applied
to the transducers in each direction and a multiple linear regression analysis was applied to
form the calibration matrix. The calibration process was based on standard procedure described
in the reference (ITTC, 2008b).
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
76
Figure 5.4. The internal force transducer calibration stand.
5.2.3 Data acquisition system and signal conditioning
The response signals from the external force transducer were recorded simultaneously and pre-
processed by the National Instrumentation data acquisition and filtering system PCI-6254M se-
ries equipped on the towing carriage. The carriage speed was also captured via an analogue
channel of this system. The data from the internal force transducer were acquired directly by
the National Instrumentation DAQ PCI-6036 fitted into the PCI slot of a desktop computer. The
data acquisition program was developed by using the LABVIEW software to capture signal from
both transducers. The sample rate were set to 100 Hz and 200 Hz for the internal and external
force transducer respectively. The sampling times were set for 20 seconds. The high frequency
noise from the system vibration were removed by applying the low-pass filter. These data were
then stored on the on-board desktop hard drive and then analysed by using Excel and
MATLAB/SimulinkTM.
5.2.4 Experimental program
The objectives of the experiment were to investigate the CCPP performance characteristics by
conducting the bollard pull and captive model tests. The tests included the measurements of
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
77
forces and moments generated by the CCPP over the range of propeller rotational speed, CCPP
pitch settings and towing carriage speed.
The experiments were conducted in accordance with the ITTC recommended procedures and
guidelines, Propulsion/Bollard Pull Test (ITTC, 2011a), Captive Model Test Procedure (ITTC,
2014) and Resistance Test (ITTC, 2011b).
In the bollard pull tests with the towing carriage at a standstill, the experiments were performed
at the propeller rotational speed of 100 RPM, 200 RPM, 300 RPM, 400 RPM and 500 RPM with
the collective angles col from 29 ( 100%) to 29 (100%) in the increments of 25% and cyclic
angles cyc from 20 ( 100%) to 20 (100%) in the increments of 25%. In the captive model
tests, the collective and cyclic angles were adjusted at fixed values prior to each run while the
propeller rotational speed and the towing carriage speed were set at specific values. The tests
were conducted at different advance coefficient J ranging from 0J to 1.5.J The propeller
collective and cyclic angles settings were varied similarly to the bollard pull condition’s settings.
The resistance test was also conducted to calculate the total resistance resulted from the under-
water vehicle model hull and the connecting struts. In the resistance tests, the model was towed
in both the forward and reverse directions with the similar advance coefficients in the captive
model tests. 2000 runs were performed in total during the two weeks of testing.
5.2.5 Data reduction and representation
The collected raw data from transducer were corrected for zero offset and then multiplied by
the calibration matrix to determine the forces and moments. These values were then averaged
over a steady period. The non-dimensional coefficients describing the propulsor performance
derived from the experimental data are defined as (Carlton, 2012):
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
78
A
VJ
nD (5.1)
2 4T X
XK K
n D (5.2)
2 4Y
YK
n D (5.3)
2 4Z
ZK
n D (5.4)
2 5Q K
KK K
n D (5.5)
2 5M
MK
n D (5.6)
2 5N
NK
n D (5.7)
where J is the advance coefficient, ( )n rps is the propeller rotational speed, (m)D is the pro-
peller diameter, (m/s)A
V is the vehicle advance speed, and 3 (kg/m ) is the water density.
In addition, the open water efficiency is defined as:
2T
Q
K J
K
(5.8)
5.2.6 Error analysis
An elementary error analysis on the experimental data were conducted in accordance with the
ITTC recommended procedures for uncertainty analysis (ITTC, 2002). The total uncertainty in
the thrust and torque coefficient U respectively were calculated from the precision error P and
the bias error .B The precision error was approximated by conducting repeated tests in specific
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
79
conditions. The bias error consists of the errors resulted from the transducer sensitivity in meas-
urements of water temperature, propeller diameter, carriage speed, propeller rotational speed,
thrust, and torque. The total uncertainties for thrust and torque coefficients are estimated as 2.4%
and 3.6% respectively.
5.2 Results and Discussions
During the tests, a wide variety of the measurements was recorded and the data analysis was
conducted to present the preliminary results. The main results presented in this section are the
performance curves of thrust, torque coefficients as function of the pitch angles in bollard pull
condition, and as function of advance coefficient in captive model test condition. The values of
col and
cyc are presented in percentage for the ease of application in simulation and control
study.
5.2.1 Bollard pull test
5.2.1.1 Effect of Collective Pitch Angle Settings
Figure 5.5 shows the thrust coefficient T
K and the torque coefficient Q
K as functions of the col-
lective pitch angle col for different propeller rotational speeds ranging from 100 RPM to 500
RPM.
As can be seen in the first graph for T
K curve, the thrust magnitude increases gradually to the
maximum positive and negative values as col expands from 0 to 100% and from 0 to -100%
respectively. The T
K absolute values for the positive col is slightly higher than that of the neg-
ative col which means that the CCPP produce more thrust in forward direction than in the re-
verse direction. There is also a difference in the torque coefficient Q
K as col varied from -100%
to 100%. The reason for the differences in T
K and Q
K at positive and negative col is due to the
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
80
flow recirculation resulted from the hull interaction. Moreover, as previously noted, the rake
angle makes the CCPP asymmetrical in the rotational plane which causes the lower reverse
thrust.
Figure 5.5. Effect of Collective Pitch Angle Settings to T
K and Q
K .
In addition, it can be seen that at a particular ,col
T
K increases as rotational speed n decreases.
For the fixed pitch propeller (FPP), changing the rotational speed is the only way to adjust the
thrust magnitude. On the other hand, for the CCPP, the thrust magnitude and direction could
be changed by controlling the combination of the rotational speed and the collective pitch angles.
This mechanism is found to be similar to the CPP, which offers significant advantages such as
the capability to gain high efficiency at different cruising speed, high thrust rate of change, flex-
ibility in straight-line motion with both forward and reverse direction, stability in the power
generation by not changing the rotor shaft speed continuously.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
81
5.2.1.2 Effect of horizontal cyclic pitch angle settings
In Figure 5.6, the horizontal force coefficient Y
K is plotted against the cyclic pitch angle ,cyc
which are presented in percentage for a range of different rotational speeds.
Figure 5.6. Effect of horizontal cyclic pitch angle settings.
The results show that the Y
K absolute value increases as cyc ranging from -100% to 100% the
limitation at both ends. The positive cyc settings would result in a horizontal force to starboard
with positive Y
K . On the contrary, the negative cyc would result in a horizontal force to the
port. This trend is observed at every rotational speed setting.
In addition,Y
K increases with the decrease of rotational speed. However, at the high rotational
speeds, above 300 RPM, Y
K appears to be independent of rotational speed to within the exper-
imental errors in this data.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
82
5.2.1.3 Effect of vertical cyclic pitch angle settings
Figure 5.7 illustrates the relationship between the vertical force coefficient Z
K and the cyclic
pitch angle cyc presented in percentage for a range of propeller rotational speeds.
Figure 5.7. Effect of Vertical Cyclic Pitch Angle Settings.
It can be seen that the results show the similar trend in the CCPP side force performance, which
has been observed in the previous case. The positive cyc settings would result in a vertical force
upwards with positive Z
K . On the contrary, the negative cyc would result in a vertical force
downwards.
In the cases of pure cyclic pitch angle settings, it could be concluded that CCPP are able to gen-
erate a significant side forces, which are observed with steady trend. Nevertheless, increasing
the rotational speed would result in the dramatic decrease in the side forces, horizontal force
and vertical force.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
83
5.2.1.4 Effect of collective and horizontal cyclic pitch angle settings
Considering the effect of both collective and horizontal cyclic pitch angle setting to the CCPP
horizontal force and thrust, Figure 5.8 shows the relationship between the horizontal force co-
efficient Y
K and cyclic pitch angle at various collective pitch angles.
Figure 5.8. Effect of collective and horizontal cyclic pitch angle settings.
From the figure it can be seen that at the positive ,col
in the range of cyc from -100% to 100%,
the CCPP has the horizontal force performance in the same fashion as in the pure cyclic settings
discussed in previous section. However, at the negative ,col
the horizontal force direction
changes in the opposite manner. The positive cyc settings would result in a horizontal force to
the port with negative Y
K . On the contrary, the negative cyc would result in a horizontal force
to the starboard.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
84
It also noted that the cyc does not have dramatic influence on thrust at different
col settings.
This means that the underwater vehicles equipped with CCPP would be able to make a turning
manoeuvre without loss in thrust.
5.2.1.5 Effect of collective and vertical cyclic pitch angle settings
Similarly to the previous case, the relationship between the vertical force coefficient Z
K and cy-
clic pitch angle at various collective pitch angles is presented in Figure 5.9.
Figure 5.9. Effect of collective and vertical cyclic pitch angle settings.
Similar to the horizontal force coefficient, the vertical force coefficient is affected by the change
of cyc at different .
col At the positive ,
col the CCPP has the vertical force performance in the
same way to the pure cyclic settings. At the negative ,col
the positive cyc settings would result
in a vertical force downwards with negative .Z
K On the contrary, the negative cyc would result
in a horizontal force upwards.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
85
In both cases of horizontal force and vertical force performance from the effect of the cyclic pitch
angle, it could be concluded that the CCPP is able to generate effective side forces with and
without the presence of thrust. In contrast to the FPP, CPP and vectored thrusters, these propul-
sors only produce thrust effectively in one direction. This feature enable the manoeuvrability of
underwater vehicle at various operational conditions, low speed and cruising speed.
5.2.2 Captive model test
5.2.2.1 Effect of collective pitch angle settings
Figure 5.10 and Figure 5.11 show the thrust coefficient T
K and torque coefficient Q
K as the func-
tion of advance coefficient J for a range of the collective pitch angle ,col
which is presented in
percentage. In the captive model experiment, the rotational speed was maintained as constant
during the tests.
Figure 5.10. Effect of positive collective pitch angle settings.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
86
As can be seen in the graphs for T
K with positive and negative col , the thrust coefficients de-
creases and increases gradually in absolute values as J increases respectively. Advance coeffi-
cient J dramatically influences T
K . The presented characteristics curve of CCPP is found to be
similar to that of the conventional propeller. It is noted that at a specific ,JT
K increases with
the rise of .col
The torque coefficient Q
K curves have the similar tendency as the thrust coeffi-
cient curves.
Figure 5.11. Effect of negative collective pitch angle settings.
The difference in the forward and reverse thrust with the positive and negative col has been
discussed in the previous section. The ability to rapidly generate significant reverse thrust could
assist the underwater vehicle in the crash-back manoeuvre as well as in the stopping manoeuvre.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
87
Figure 5.12. Maximum open water efficiency of CCPP in the range of advance coefficient.
The maximum open water efficiency of CCPP for different positive collective pitch settings,
shown in Figure 5.12, are presented in the range of advance coefficient. The experimental results
show that CCPP has the maximum efficiency at 0.2, 0.4, 0.6J with 75%col and at
0.8, 1.0, 1.2J with 100%.J In general, the maximum open water efficiency of CCPP is
0.73 at 1J with the collective pitch setting 100%.col
5.2.2.2 Effect of horizontal cyclic pitch angle settings
The relationship between the horizontal force coefficient Y
K and the advance coefficient J for
different cyclic pitch angle settings is presented in Figure 5.13.
It is interesting to note that Y
K sharply increases its absolute value as J increases. The reason
for this characteristics is that it is due to the effect of water inflow velocity which alter the lift
generated on each blade of the CCPP. Additionally, in a particular J value, the performance is
consistent with the bollard pull condition.
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
88
Figure 5.13. Effect of horizontal cyclic pitch angle settings.
5.2.2.3 Effect of vertical cyclic pitch angle settings
Similar to the previous section, the effect of vertical cyclic pitch angle settings on the CCPP per-
formance is illustrated in Figure 5.14 by plotting the vertical force coefficient Z
K against the ad-
vance coefficient J for a range of cyclic pitch angles .cyc
The behaviour of the vertical force coefficient Z
K with respect to J is similar to the behaviour
of the horizontal force coefficient Y
K . It can be found that the side force coefficients, Y
K and Z
K ,
are not only dependent on cyc but also on .J These results suggest that the side forces could be
controlled by both variables cyc and J for the optimum performance.
Generally, the findings from the captive model test show a fairly consistent CCPP performance
in the range of advance coefficients as in the bollard pull condition. In the underwater vehicle
simulation at different manoeuvring, all effects have to be taken into account for the accurate
performance prediction. The obtained empirical values can be analysed and saved in the form
Chapter 5. Experimental Study of the Collective and Cyclic Pitch Propeller
89
of look-up table which predict the CCPP manoeuvring forces as a function of pitch angle settings
and advance coefficient.
Figure 5.14. Effect of vertical cyclic pitch angle settings.
5.3 Summary
A series of comprehensive bollard pull and captive model tests were designed and conducted
on the innovative propulsor named CCPP to evaluate its performance. The effects of the collec-
tive and cyclic pitch settings on the CCPP performance have been examined and discussed. Ac-
cording to the obtained results, it is shown that the CCPP is capable of generate an effective
manoeuvring forces in both bollard pull and captive model conditions. The results also provide
an insight into the relationship between these manoeuvring forces and controlled parameters
that enables the simulation and control study of the underwater vehicle equipped with CCPP.
As part of the research project, the experimental results from this study is used in a comparison
study with experimental data of FPP to evaluate the effectiveness of an underwater vehicle per-
formance
90
CHAPTER 6
Manoeuvring Simulation
In chapter 6, an AUV simulation program named AUVSIPRO is proposed in the preliminary
design stage to predict and compare the AUV manoeuvrability equipped with different propul-
sion configurations. A series of primary manoeuvres standard for underwater vehicles are pre-
sented to investigate the system feasibility. In order to derive the mathematical model in the
simulator, the propulsor models are experimentally conducted in the towing tank, the hull hy-
drodynamic coefficients are calculated using analytical, and system identification approaches.
The system outputs are achieved by numerical method. The simulation program provides an
effective platform to examine different the propulsion system configurations to an AUV as well
as a torpedo shaped submarine.
Part of this chapter has been presented at “The Forth International Conference on Modelling and
Simulation for Autonomous System in Rome, Italy 2017” and has been submitted to the “Ocean En-
gineering, An International Journal of Research and Development”. Citations for conference paper
and journal paper are:
91
Tran M, Binns J, Chai S, et al. (2017). AUVSIPRO–A Simulation Program for Performance Pre-
diction of Autonomous Underwater Vehicle with Different Propulsion System Configurations.
International Conference on Modelling and Simulation for Autonomous Systems. Springer, 72-82.
Minh Tran, Hung Nguyen, Jonathan Binns, Shuhong Chai and Alex Forrest, A comparison study
of two propulsion system configurations for an autonomous underwater vehicle, Ocean Engi-
neering, An International Journal of Research and Development.
Chapter 6. Manoeuvring Simulation
92
6.1 Introduction
In this chapter, a simulation program named AUVSIPRO is proposed using the
MATLAB/SimulinkTM. The program is able to rapidly simulate the underwater vehicle equipped
with different propulsion systems in various defined standard manoeuvrability. This would
greatly facilitate the design of vehicle propulsion system and provide a good understanding of
the performance of an AUV. In addition, a wide range of control strategies could be applied in
AUVSIPRO to validate the vehicle performance prior to practical implementation.
The chapter is structured as follows: Section 2 briefly describe the basic components and features
of AUVSIPRO. A general description of the mathematical model of an underwater vehicle in-
corporated in AUVSIPRO is presented in Section 3. Fundamental manoeuvrability to examine
an underwater vehicle performance are proposed and the simulation results are presented in
section 4. Section 5 summarises the chapter.
6.2 AUVSIPRO – The Simulation Program Description
The AUVSIPRO is built using SimulinkTM blocks and a set of MATLABTM defined functions as
shown in Figure 6.1. There are five basic components in the program including the propulsion
system blocks, vehicle dynamic blocks, transformation blocks, display blocks and output-saving
blocks. These components are coloured in orange, cyan, white, yellow and blue respectively for
the easy of presentation.
The main component is the vehicle dynamic block, which describes the equations of motion and
dynamic model of an underwater vehicle. The Gavia AUV is selected as the vehicle platform for
the simulation in this study. In addition to the Gavia AUV, the AUVSIPRO also includes other
underwater vehicle model such as REMUS AUV presented in different parameter block.
Chapter 6. Manoeuvring Simulation
93
The propulsion system component consists of the input control signals and the mathematical
model relating the inputs to the corresponding generated forces. There are two different pro-
pulsion systems examined in the study including the conventional propulsion system with FPP
and the CCPP.
In the propulsion system block, the control signals were defined using the Signal Builder block
as shown in Figure 6.2. A series of Signal Builder blocks were built in accordance with the fun-
damental manoeuvring ability tests, which were illustrated in next section. In the FPP propul-
sion module, the empirical model developed in chapter 4 was utilised. It should be noted that a
minor modification was made to the FPP mathematical model in AUVSIPRO due to the presence
of the duct in the FPP configuration. The tested propeller was utilised to operate inside a Nau-
tican accelerating nozzle. Since this nozzle is equipped with supporting mechanical and electri-
cal components in the propulsion unit the experiment to measure the nozzle thrust could not be
conducted. It is known that the accelerating flow type of nozzle itself produces a positive thrust
and offers a means of increasing the efficiency of open propellers (Oosterveld, 1970). Compared
to open propeller with the same design conditions, a nozzle can produce between 25% and 30%
more thrust at towing speed (Bose, 2008). These estimated values would be used to modify the
nozzle effect to the open propeller in the AUVSIPRO as the experimental data are not currently
available. In this study, the value of 25% were applied in the simulation model.
In the CCPP propulsion block, the Lookup Table blocks were utilised to construct the propulsion
mathematical model, shown in Figure 6.3. In the Lookup Table, the relationship between the input
control signals and output forces were presented based on the experimental data in chapter 5.
The output signals from these propulsion system blocks were then sent to the dynamic block to
form the complete equations of motions. Using the pre-defined hydrodynamic coefficients, the
Chapter 6. Manoeuvring Simulation
94
differential equations were solved and integrated in the transformation blocks to provide the
vehicle state values such as positions and velocities.
Figure 6.1. The layout of the AUVSIPRO Simulink Model.
Figure 6.2. The Signal Builder block as the input signal in the propulsion component.
Chapter 6. Manoeuvring Simulation
95
Figure 6.3. The Lookup Table block representing the CCPP system mathematical model.
In the simulation program, the general AUV equations of motion developed from the Chapter
3 are converted into the standard state-space equations in the simulation program. The state-
space equations are presented as follows:
( )
-1
J η υη
υ M -C υ D υ υ g η τ (6.1)
The general non-linear matrix-vector form is:
,x F x u (6.2)
where x is the state vector and u is the control input signal.
Chapter 6. Manoeuvring Simulation
96
The Runge-Kutta numerical integration is utilised to numerically solve the underwater vehicle
equations of motion. The continuous equation (6.2) is defined in the discrete time domain as:
,n n n
x f x u (6.3)
where n
x is the state vector, and n
u is the input control vector.
In the Runge-Kutta Fourth-order method, the following equations are calculated:
1,
n n nk x f x u
2 1 1/2,
2 n
tk f x k u
3 2 1/2,
2 n
tk f x k u
4 4 1,
nk f x tk u
(6.4)
where the interpolated vector is
1/2 1
1
2n n nu u u
(6.5)
State vector at 1n
x
is calculated based on state vector n
x as:
1 1 2 3 42 2
6n n
tx x k k k k
(6.6)
It is also noted that the current effects on the AUV in the simulation have not been included in
the open loop simulation. In the context of the comparison study between the two systems, this
effect is assumed not significant.
Chapter 6. Manoeuvring Simulation
97
6.3 Manoeuvring Design
The basic concept behind the manoeuvring of a submarine are very similar to that of a surface
ship (Renilson, 2015). In general, there are typical manoeuvres applied to examine the manoeu-
vrability and performance characteristics of an underwater vehicle, including the acceleration
manoeuvre, stopping manoeuvre, turning circle manoeuvre, static turning manoeuvre, pull-out
manoeuvre, zig-zag manoeuvre, depth-changing manoeuvre, meander manoeuvre, spiral ma-
noeuvre and reverse spiral manoeuvre.
6.3.1 Acceleration Manoeuvre Test
This test illustrates how the AUV travel during acceleration. An acceleration test is performed
by increasing the speed of the AUV from rest or from a particular ahead speed to a higher ahead
speed (Issac et al., 2007; Lewis, 1988). The acceleration test is important for vehicles that may
have a change position rapidly or accelerate suddenly for a mission (Lewis, 1988).
Figure 6.4. Acceleration Test.
Chapter 6. Manoeuvring Simulation
98
6.3.2 Stopping Test
Stopping is the manoeuvre of interest primarily from the point of view of avoiding collisions,
rammings, and groundings (Lewis, 1988). The most common manoeuvre in stopping test is the
crash-stop from full ahead speed (Bertram, 2012) . For the vehicle equipped with FPP, the motor
is stopped and then reversed at full astern. Additionally, for the AUV with large control surfaces,
the stopping characteristics can be improved by fluctuating the control surfaces to increase drag
resulted from the hull and the control surfaces themselves. The AUV equipped with CCPP con-
figuration can perform the stopping manoeuvre by two methods. In the first method, similar to
the conventional FPP configuration, the propeller direction is reversed to obtain a crashback
condition. In the second method, the collective pitch angles are changed to the negative setting
and the motor speed remains constant. This feature is unique to the CCPP or the controllable
pitch propeller in general. In these two methods, the latter method has the better performance
since it takes more time for the CCPP to slow to zero and then reverse the rotation direction to
reach a new speed in the first method. Moreover, the second method is selected for the simula-
tion study due to the availability of experimental data conducted in previous chapters.
Figure 6.5. Stopping Test.
Chapter 6. Manoeuvring Simulation
99
6.3.3 Turning Circle Manoeuvre
The turning circle manoeuvre is a measure of the ability to turn the underwater vehicle in a
certain setting of the propulsion system. The turning circle manoeuvre is to be perform to both
starboard and port with the maximum design rudder angle or maximum cyclic pitch setting for
CCPP permissible at the test speed. The control action is executed following a steady approach
with zero yaw rate. The essential information to be obtained from this manoeuvre is tactical
diameter, advance, and transfer (IMO, 2002).
Figure 6.6. Turning Circle Manoeuvre Test.
Chapter 6. Manoeuvring Simulation
100
6.3.4 Static Turning Manoeuvre
The static turning circle manoeuvre is executed as the underwater vehicle accelerating from rest.
The static turning manoeuvre is an important manoeuvre in the low speed operation of an AUV.
In the static turning, the thrust and manoeuvring forces such as side forces are taken in consid-
eration as the AUV needs to rotate in the case of hovering and turning around or avoiding col-
lision, and receiving the updated control measures.
Figure 6.7. Static Turning Manoeuvre Test.
6.3.5 Pull-out Manoeuvre
The pull-out manoeuvre is used as a test to indicate the underwater vehicle’s yaw stability. After
a turning circle with steady rate of turn, the manoeuvring forces are disabled. If the vehicle is
yaw stable, the rate of turn will decay to zero for turns both port and starboard. If the vehicle is
yaw unstable, the rate of turn will reduce to some residual rate of turn (Bertram, 2012).
6.3.6 Zig-Zag Manoeuvre
The zig-zag manoeuvre is conducted to indicate the course-changing (horizontal plane) ability
of the marine vehicle. For a zig-zag test in the horizontal plane, the rudder is deflected to a
Chapter 6. Manoeuvring Simulation
101
constant angle, 0
, as quickly and smoothly as possible and maintained at this angle until the
change in the heading becomes 0. The rudder is then deflected to
0 and held steady until
the vehicle’s heading has changed to 0. For a zig-zag in the vertical plane the stern planes are
deflected instead of the rudder, and a specified change in pitch is used instead of change in
heading (Renilson, 2015). For the underwater vehicle equipped with CCPP, the manoeuvring
forces to perform the zig-zag test are obtained from the CCPP cyclic pitch setting instead of the
control surfaces in the conventional propulsion. The CCPP is adjusted to a constant cyclic angle
cyc similar to
0.
Figure 6.8. Zig-Zag Manoeuvre Test.
6.3.7 Depth-changing manoeuvre
It is important to perform the depth-changing test for the underwater vehicle to examine its
diving ability. This manoeuvre is particular to the underwater vehicle and is conducted by
changing the control surface angles and the cyclic pitch angle so that the vehicle is able to reach
a certain depth in the vertical plane. This manoeuvre is used to represent the combined thrust
and side force effects that the configuration has on the ability to rapidly change depth from a
certain depth to a different depth from which the AUV will conduct other operations.
Chapter 6. Manoeuvring Simulation
102
Figure 6.9. Depth-Changing Manoeuvre Test.
6.3.8 Meander Manoeuvre
The meander manoeuvre is similar to the zig-zag manoeuvre in the vertical plane, with the dif-
ference that once the execute pitch angle is reached, the manoeuvring control forces are brought
to zero (and not reversed as in the zig-zag test) (Renilson, 2015). The objective of this test is to
examine the ability of the underwater vehicle to return to a stable state after a disturbance to the
pitch angle in the vertical plane.
Figure 6.10. Meander manoeuvre test.
Chapter 6. Manoeuvring Simulation
103
6.3.9 Spiral Manoeuvre or Helix Manoeuvre
The spiral manoeuvre is considered a complex manoeuvre, which combines the heading and
diving manoeuvre. For the underwater vehicle actuated by the conventional propulsion system,
the rudder and stern plane are deflected to specific angles at the same time. For the vehicle
equipped with CCPP, both the vertical and horizontal cyclic pitch settings are enabled. The spi-
ral manoeuvre is not a standard manoeuvre but is designed to excite all 6 DOF (Issac et al., 2007)
and also to examine the combination of all control actuators.
Figure 6.11. Spiral Manoeuvre Test.
Chapter 6. Manoeuvring Simulation
104
6.3.10 Reverse Spiral
The rudder angle required to achieve a given yaw rate is determined. This is then repeated for
a range of different yaw angles (Renilson, 2015).
6.4 Results and Discussion
In this section, the numerical simulation results for important manoeuvres are presented for
both the conventional FPP and the CCPP propulsion system applied to the Gavia AUV platform.
The analysis aims to investigate various manoeuvrability qualities of the two propulsion con-
figurations and their impacts on the AUV manoeuvring. The manoeuvring performance is eval-
uated based on the typical parameters traditionally adopted in marine vehicle manoeuvring.
All the simulations were assumed to be conducted at a certain depth in which the effects of the
free surface were rather small and could be neglected. The maximum collective pitch angle were
selected for the most of the simulated scenario to stress the best performance characteristic. Nev-
ertheless, in practical operation when the power consumption problem is of interest, the opti-
mization process is needed to balance the manoeuvring capability and power efficiency. The
lower collective pitch angle setting in the range of 50% to 75% would be more appropriate.
The selected manoeuvres for the simulation study are the most common manoeuvres to high-
light the differences in performance between the two systems. The comparison is addressed and
discussed thoroughly in the following section.
6.4.1 Acceleration Manoeuvre Test
In the acceleration test, the vessel starts with initial velocities 0 0 0
0u v w and the com-
manded constant propeller revolution speed. The AUV simulation model was set with the com-
manded input propeller speeds of 500 RPM, 700 RPM and 900 RPM. The simulation time was
about 50 seconds for each case.
Chapter 6. Manoeuvring Simulation
105
Figure 6.12 and Figure 6.13 show the travel distance and forward speed of an AUV with FPP in
the acceleration test. As can be seen in Figure 6.12, the maximum steady forward speeds are 1.2
m/s, 1.6 m/s and 2 m/s for the cases of 500 RPM, 700 RPM and 900 RPM respectively. The time
taken to approach these maximum speeds is approximately 35 seconds as shown in Figure 6.13.
Figure 6.14 and Figure 6.15 show the travel distance and forward speed of an AUV with CCPP
at 50% collective pitch setting in the acceleration simulation test. It can be seen in Figure 6.14,
the maximum steady forward speeds are about 0.6 m/s, 0.82 m/s and 1.1 m/s for the cases of 500
RPM, 700 RPM and 900 RPM respectively. The time taken to approach these maximum speeds
is approximately 25 seconds as shown in Figure 6.15.
Figure 6.16 and Figure 6.17 show the travel distance and forward speed of an AUV with CCPP
at 100% collective pitch setting in the acceleration simulation test. In 100% collective pitch setting
case, the CCPP generates the maximum thrust. It can be seen in Figure 6.16, the maximum
steady forward speeds are about 1.05 m/s, 1.42 m/s and 1.9 m/s for the cases of 500 RPM, 700
RPM and 900 RPM respectively. The time taken to approach these maximum speeds is approx-
imately 15 seconds as shown in Figure 6.17.
The AUV with CCPP has the lower acceleration time or faster response compared to the AUV
with conventional FPP. At 900 RPM, the AUV with CCPP at 100% collective pitch angle achieves
1.9 m/s in 20 seconds. On the other hand, the AUV with FPP reaches 2 m/s distance within 30
seconds. Generally, the CCPP with its maximum collective pitch setting has a slightly higher
obtained forward speed compared to the FPP at a given propeller rotational speed. However,
the CCPP has a faster speed response as the control input signal is applied which suggests that
the AUV with CCPP has a better acceleration capability. This feature is critical to the underwater
vehicle operating in a confined environment at low speed condition.
Chapter 6. Manoeuvring Simulation
106
The simulation data also show a linear increase in distance as the propeller rotational speed
increases. During the acceleration manoeuvre, the AUV pitch and roll angle are in the limited
regions. The Gavia AUV seems to have appropriate vertical stability in the tests with no ten-
dency to increase the overshoot in both propulsion configurations. The travelling altitude is rel-
atively constant. The heave velocity reaches to 0.2 m/s as the AUV starts to move and then drops
to nearly 0 m/s as the AUV attains a steady state surge velocity.
Figure 6.12. The travel distance of an AUV with FPP in the acceleration simulation test.
Chapter 6. Manoeuvring Simulation
107
Figure 6.13. The forward speed of an AUV with FPP in the acceleration simulation test.
Figure 6.14. The travel distance of an AUV with CCPP at 50% collective pitch setting in the ac-
celeration simulation test.
Chapter 6. Manoeuvring Simulation
108
Figure 6.15. The forward speed of an AUV with CCPP at 50% collective pitch setting in the ac-
celeration simulation test.
Figure 6.16. The travel distance of an AUV with CCPP at 100% collective pitch setting in the
acceleration simulation test.
Chapter 6. Manoeuvring Simulation
109
Figure 6.17. The forward speed of an AUV with CCPP at 50% collective pitch setting in the ac-
celeration simulation test.
6.4.2 Stopping Manoeuvre Test
In stopping test simulation, the AUV was forced to stop from the steady forward velocity of 1.5
m/s. The simulation time was about 50 seconds for each case. The results of the deceleration and
stopping of Gavia AUV with conventional FPP and CCPP propulsion system follow an expected
pattern in the simulation.
To decelerate and stop an underwater vehicle with the conventional FPP propulsion, a crash-
back on the FPP was applied. In the crashback manoeuvre, the FPP rotational speed is reversed
to negative value as the AUV is moving forward and the control surfaces are at neutral position.
The stopping distance and stopping time versus propeller rotational speed RPM for the AUV
with FPP in the stopping simulation test are shown in Figure 6.18 and Figure 6.19, respectively.
It can be seen in Figure 6.18, the stopping distance values are about 18 m, 22 m, and 27 m for the
cases of -500 RPM, -300 RPM, and -100 RPM, respectively. The corresponding stopping time
Chapter 6. Manoeuvring Simulation
110
values shown in Figure 6.19 are 15 seconds, 20 seconds, and 23 seconds. The results show that
the distance and time to stop is highly depend on the propeller negative rotational speeds.
Figure 6.20 and Figure 6.21 show stopping distance and stopping time versus cyclic pitch angle
for the AUV with CCPP in the stopping simulation test. As can be seen in Figure 6.20, at CCPP
rotational speed 300 RPM, the stopping distance values are about 13 m, 21 m, and 22 m for the
cases of -100%, -50%, and -25%, respectively. At rotational speed 500 RPM, the stopping distance
values are about 7 m, 11 m, and 12 m for the cases of -100%, -50%, and -25%, respectively. The
distance and time to stop are depend on not only the propeller rotational speeds but also the
cyclic pitch angle.
The minimum time to stop for the CCPP as shown in Figure 6.21 is 8 seconds. In this case, it
takes approximately three vehicle’s lengths to stop. The CCPP’s minimum stopping time value
is just haft of the FPP’s value. The shorter stopping distance and time are due to the faster de-
celeration rate. The CCPP has a higher deceleration rate as the reversed thrust from CCPP rap-
idly increases by changing the collective pitch angle. For the FPP, the motor has to stop and the
thrust in reverse direction gradually increases as the rotational speed increases.
The stopping manoeuvre for both propulsion configuration could also be conducted by simply
switching off the propeller speed. During this time, the AUV decelerates and stops mainly due
to the hull frictional resistance. The simulation also shows that the vehicle was able to hold a
consistent depth during the stopping manoeuvre. The simulated depth values were around the
initial depth since the buoyancy force was adjusted to be equal the weight and the ability to keep
balance of the vehicle. This feature is important for the intervention task in which the vehicle is
required to approach the exact location in a working area or to stop at the exact recovery position.
Chapter 6. Manoeuvring Simulation
111
Figure 6.18. The stopping distance versus propeller RPM for the AUV with FPP in the stop-
ping simulation test.
Figure 6.19. The stopping time versus propeller RPM for the AUV with FPP in the stopping
simulation test.
Chapter 6. Manoeuvring Simulation
112
Figure 6.20. The stopping distance versus cyclic angle for the AUV with CCPP in the stopping
simulation test.
Figure 6.21. The stopping time versus cyclic angle for the AUV with CCPP in the stopping sim-
ulation test.
Chapter 6. Manoeuvring Simulation
113
6.4.3 Static Turning Manoeuvre
The turning characteristics of an AUV at low speed are characterised based on the static turning
manoeuvre. The standard parameter measured was the steady turning diameter .d In this sec-
tion, a series of runs was conducted to characterise the turning performance of the AUV
equipped with FPP and CCPP.
The AUV starts the static turning manoeuvre at a constant depth by maintaining a constant con-
trol surface angle or a steady cyclic pitch angle in the case of the CCPP from the stationary con-
dition.
The results for the turning diameter of the Gavia AUV equipped with conventional FPP propul-
sion system are shown in Figure 6.22. In this plot, the variation of the turning diameter is plotted
versus the average control surface deflection angles at different propeller rotation speeds. In the
simulation, the average control surface deflection angle were applied to all four planes, which
are 5 , 10 , 15 , and 20 .
Figure 6.22. The turning diameter versus deflection angle for the AUV with FPP.
Chapter 6. Manoeuvring Simulation
114
Figure 6.23. The turning diameter versus cyclic angle for the AUV with CCPP.
It can be seen from Figure 6.22 that the turning diameter becomes smaller for the larger control
surface deflection angle. The maximum turning diameter is about 140 m at 05 deflection for all
four speeds and the minimum turning diameter is 55 m at 020 deflection angle and 900 RPM. It
is also be noted that the turning diameter does not depend notably on the propeller rotation
speed or the surge. For the small deflection angles, the examined diameters are identical. For
the larger deflection angle, the turning diameter increases as the rotation speed increases. Hence,
for the AUV equipped with conventional FPP propulsion system, the deflection angle has a sig-
nificant impact on the turning characteristics of the AUV compared to the vehicle speed. In ad-
dition, there is the speed loss as the turn progresses. In practice, this speed loss is expected and
due to the combined effects of the added drag on the hull due to cross flow as well as the added
drag due to the rudder deflection (Heberley, 2011).
The results for the turning diameter of the Gavia AUV equipped with CCPP propulsion system
are shown in Figure 6.23. In this plot, the variation of the turning diameter is plotted versus the
Chapter 6. Manoeuvring Simulation
115
cyclic pitch angle at different propeller rotation speeds. In the simulation, three cyclic pitch an-
gles were investigated, which are at 25%, 59%, and 100%. The collective pitch angle was kept
constant at 100%.
Similar to the FPP, it can be seen from Figure 6.23 that the turning diameter becomes smaller for
the larger cyclic pitch angle. The maximum turning diameter is about 23 m at 25% cyclic pitch
angle and 500 RPM. The minimum turning diameter is 15 m at 100% cyclic pitch angle and 900
RPM. For the AUV equipped with CCPP propulsion system, both the cyclic pitch angle and the
CCPP rotation speed have a significant impact on the turning characteristics of the AUV. The
turning diameter increases as the CCPP rotation speed increases.
It can be seen from Figure 6.22 and Figure 6.23 that the AUV with CCPP has a greater turning
characteristic in the static turning manoeuvre. The minimum turning diameter for the AUV with
CCPP is 15 m, which is significantly smaller than that of the AUV with FPP. The turning quality
of the CCPP configuration is superior with respect to the FPP since the side force from CCPP is
generated instantly as the CCPP is rotating. On the other hand, the side force from the conven-
tional FPP propulsion system is gradually generated as the AUV speed increases from the start.
For the verification of simulated results in this section, the non-dimensional turning coefficient
is used. The non-dimensional turning coefficient d is defined as
dd
l
where l is the total length of the AUV and d is the turning diameter.
Chapter 6. Manoeuvring Simulation
116
The ISiMI AUV has the minimum 12
101.2
d (Jun et al., 2009). The MUN AUV has
2315.3
1.5d (Issac et al., 2007). In our study, the Gavia AUV with FPP has the minimum
5522
2.5d , the Gavia AUV with CCPP has the minimum
156.
2.5d
6.4.4 Zigzag Manoeuvre
The simulation results for the zigzag manoeuvre test are presented in this section. Zigzag ma-
noeuvres are an indicative of the controllability of the vehicle (Issac et al., 2007). The main inter-
est of this manoeuvre test is to evaluate the performance of the propulsion system in generating
the continuous side forces used for heading control.
The zigzag tests are conducted with the 20-degree variation in heading angle and at a defined
constant propeller rotational speed. The manoeuvre test is called the 20/20 horizontal zigzag test.
For the AUV with FPP, the control surfaces were controlled to oscillate between the average
deflection angles of -20 degree and 20 degree. All four control surfaces rotate simultaneously.
For the CCPP, the blades are controlled in the horizontal cyclic pitch setting in the range of -20%
to 20%. Once the vehicle reaches a steady surge, the control surfaces and cyclic pitch setting are
enabled to generate the horizontal side forces. The estimation results of trajectory for the Gavia
AUV equipped with FPP and CCPP in the zigzag test are plotted in Figure 6.24.
The simulation results show that the overshoot angles for both configurations are in the range
of 3 to 6 degree. It can be seen from Figure 6.24 that the heading angle of the AUV with CCPP
has a smaller overshoot angle when compared to the AUV with conventional FPP.
Chapter 6. Manoeuvring Simulation
117
Figure 6.24. Zigzag test of AUV equipped with FPP and CCPP.
In addition, for the FPP, the commanded amplitude and cycle-length for the zigzag are about 34
m and 60 m respectively. For the CCPP, the commanded amplitude and cycle-length are ap-
proximately 10 m and 30 m. The smaller cycle-length and smaller overshoot mean that the CCPP
has the better manoeuvring capability by combining continuous thrust and side forces in head-
ing control. The reason is the effect of the side force magnitude of the CCPP is higher and espe-
cially the faster response of the side force from CCPP compared to FPP. It is also noted that in
the AUV with CCPP configuration, the vehicle’s state variables in heave direction were not sig-
nificantly influenced as the zigzag manoeuvre was conducted. Moreover, in the zigzag manoeu-
vre test the forward velocity of the AUV decreases from the cruising velocity to an unsteady
velocity during the turning. This reduction in speed is expected due to the increasing of drag in
such a manoeuvre.
The zigzag test simulation for the AUV equipped with CCPP at low propeller rotational speed
100 RPM and small collective pitch setting of 20% was conducted. It was found that the AUV
has the lower cycle-length of 45% compared to the previous case with maximum collective pitch
Chapter 6. Manoeuvring Simulation
118
setting and high RPM. Hence, it is proved that the CCPP is capable of providing low enough
continuous thrust to enable the low speeds desirable for precision manoeuvring and inspection
tasks.
6.4.5 Depth-Changing Manoeuvre
For the comparison of the depth changing abilities between the AUV equipped with FPP and
with CCPP, the following manoeuvre is conducted. To address the comparison between the two
configurations, the depth variation in time series under the input control signal was simulated
and analysed.
In the depth-changing manoeuvre simulation, the AUV’s pitch angle was limited to 20 degree.
The AUV was initially set to travel a straight course while the control surface and cyclic angle
were executed to cause the vehicle to descend at the 25 second. After 10 seconds, the actuators
were set back to the neutral position. The simulation was set to about 75 seconds.
The time history of depth for the Gavia AUV with FPP propulsion system are shown in Figure
6.25. The depth variable is presented as the function of the propeller rotational speed and control
surface deflection angle. It can be seen from Figure 6.25 that the larger depth are obtained for
the higher rotational speed and deflection angle.
Figure 6.26 shows the variation of depth change for the Gavia AUV with CCPP propulsion sys-
tem. The depth variable is presented as the function of the propeller rotational speed and the
vertical cyclic pitch angle. In this manoeuvre, the collective pitch angle was controlled to 100%
setting for the maximum thrust generation at a given CCPP rotational speed. As can be seen on
the Figure 6.26, after the first execution of the cyclic setting, the AUV starts to descend after a
time delay of approximately 4 seconds. It can be seen from Figure 6.26 that the larger depth are
obtained for the higher rotational speed and cyclic pitch angle.
Chapter 6. Manoeuvring Simulation
119
It is obvious that the magnitude of obtained depths are much higher for the CCPP configuration
than for the FPP configuration with a given propeller rotational speed in a specific time. For
example, the CCPP configuration with 100% cyclic pitch setting and rotational speed of 700 RPM
is able to reach the 20 meter depth in 18 seconds. On the other hand, the FPP configuration with
20 degree deflection angle and similar rotational speed attains 20 meter depth in approximately
40 seconds. The fundamental difference between two configurations is the quicker response of
the CCPP as the control signal is executed. In both configurations, the pitch angle oscillates at
the beginning of simulation, but get stable and fluctuate narrowly around neutral position. The
AUV with CCPP is capable of achieving the pitch faster than the FPP from the start. Nevertheless,
the CCPP with maximum collective pitch setting generates slightly lower thrust compared to
the FPP at a given propeller rotational speed in the diving manoeuvre.
Figure 6.25. The depth change simulation data for the AUV with FPP.
Chapter 6. Manoeuvring Simulation
120
Figure 6.26. The depth change simulation data for the AUV with CCPP.
6.5 Summary
In this chapter, the simulation results of the manoeuvring performance of the Gavia AUV
equipped with CCPP propulsion system were compared against the Gavia AUV equipped with
conventional FPP propulsion system. The main objective of this exercise was to find an answer
to the research question, which propulsion system is more efficient for propelling a AUV in
different manoeuvring tests.
A simulator for an underwater vehicle named AUVSIPRO was constructed in
MATLAB/SimulinkTM environment. This program is developed with the emphasis on the per-
formance prediction of an underwater vehicles equipped with different propulsion systems in
the early design stage. The AUVSIPRO could also be extended to adapt to a variety of underwa-
ter vehicles and propulsion systems for the simulation study.
Chapter 6. Manoeuvring Simulation
121
The simulation results indicated that the AUV equipped with CCPP provided better manoeu-
vrability in comparison to the AUV equipped with conventional FPP propulsion system. In the
considered manoeuvring tests, the CCPP outperformed the FPP in most of the examined pa-
rameters and variables. Five separate fundamental manoeuvring tests were presented to demon-
strate the performance differences between the two configurations. A preliminary analysis was
conducted based on the obtained results from simulation study. In the acceleration test, the re-
sults indicated that the CCPP propulsion had an advantage for high acceleration rate; mean-
while the conventional FPP propulsion was beneficial better steady forward speed. In the static
turning manoeuvre and zigzag test, there was a clear advantage with respect to the CCPP con-
figuration in terms of heading changing ability. The shorter stopping distance and time were
due to the faster deceleration rate in the stopping test showed the better stopping performance
of CCPP. The simulation results revealed that the CCPP had the superior diving characteristic
in the vertical plane.
122
CHAPTER 7
CONTROL APPLICATION
The final objective of the thesis is to execute the AUV equipped with CCPP in autonomous mis-
sions, thus the control application is considered in this chapter. While there exist numerous
works on the control of AUV, there are a few works existing for the control of an AUV with the
configuration similar to CCPP. The complex, inherently unstable and nonlinear nature of AUVs
poses significant challenges for design and implementation of a controller. The nonlinear system
obtained from previous chapters is linearized to provide an approximation to the system dy-
namics that is more approachable for control synthesis. Since the linear model of Gavia AUV is
of interest, it is more accurate to obtain the validated model directly from the experimental data
using SI compared to the first principle modelling approach discussed in Chapter 3. This ap-
proach is a relevant technique to determine the practical AUV model for designing controllers.
Chapter 7 includes the system identification (SI) of the Gavia AUV platform and the controller
design for an AUV equipped with CCPP.
To design a successful controller, it is essential to capture the AUV dynamics as accurate as
possible. In the first section, the two-stage identification of mathematical models governing dy-
namics in both vertical and horizontal planes for an axisymmetric torpedo shaped AUV are pre-
sented. The experimental data used for the system identification study are acquired from the
123
AUV on-board sensors during the field trails. The general equations for six degrees of freedom
motions are decoupled into non-interacting longitudinal and lateral subsystems in the form of
linear state space models with unknown parameters. Rather than roughly identifying the model
parameters during a certain period of time in one stage computation, the identified model is
optimised subsequently based on least squares algorithm in this study. The objective of the two-
stage system identification is to estimate simulator’s coefficients for reasonably predicting the
vehicle performance over time from a given initial condition. The accuracy of the identified
model was verified by simulation in time domain, using a set of different trial data.
The second section of this chapter aims to design an optimal state feedback controller using the
Linear Quadratic Regulator for an AUV equipped with CCPP. The development of the control
algorithms has a certain challenge due to the multivariable character of the problem. The non-
interacting longitudinal and lateral subsystems in the form of linear state space models obtained
from SI section are utilised. The propulsor dynamic models are linearised from the empirical
models in chapter 4 and 5. The control objectives are to maintain the autonomous underwater
vehicle at desired depth and heading with the CCPP. The performance of the controller is
demonstrated by simulation using MATLAB/SimulinkTM.
Part of this chapter has been published in “Proceedings of the 3rd Vietnam Conference on Control and
Automation” and in “Proceeding of the 2017 Asian Control Conference in Gold Coast, Australia”. The
citations for the conference journals are:
Minh Tran, Supun A.T. Randeni, Hung D. Nguyen, Jonathan Binns, Shuhong Chai and Alex
Forrest, Least Squares Optimisation Algorithm Based System Identification of an Autonomous
Underwater Vehicle, Proceedings of the 3rd Vietnam Conference on Control and Automation, Vietnam,
2015.
124
Tran M, Binns J, Chai S, et al. (2017). Optimal control of an autonomous underwater vehicle
equipped with the collective and cyclic pitch propeller. Control Conference (ASCC), 2017 11th
Asian. IEEE, 354-359.
Chapter 7. Control Application
125
7.1 System Identification
7.1.1 Introduction
With the objective of assessing the high-fidelity simulation of AUV with different propulsion
configurations, this section develops a two-stage system identification (SI) algorithm in order to
accurately and rapidly identify the hydrodynamic coefficients of the AUV mathematical linear
model. A precise dynamic model of an underwater vehicle is also essential for accurate autopilot
control and navigation system design.
Obtaining accurate model of an underwater vehicle is considerably complicated. There are four
fundamental methods to determine a mathematical model of an underwater vehicle. The first
method is an analytical approach to calculate the hydrodynamic coefficients by using empirical
equations and component build-up method (Prestero, 2001a). This method is a class of the first
principle approach discussed in chapter 3. The second is using Experimental Fluid Dynamic
(EFD) methods such captive model experiments (Ridao et al., 2001). The third method is con-
ducting Computational Fluid Dynamic (CFD) simulations to replicate the EFD testings (Phillips
et al., 2007; P. et al., 2015) and the final one is SI which is employed in this chapter. In the SI
method, the hydrodynamic coefficients that characterise the vehicle dynamics of an AUV could
be estimated using data acquired by on-board sensors from free running field trials (Avila et al.,
2013). The analytical and CFD approaches are generally used in the preliminary design stage to
estimate hydrodynamic coefficients of AUV based on the empirical equations and the vehicle
geometry. The use of EFD such as the experiment in the towing tank or model test basin requires
extensive time and high cost for the setup and testing. On the other hand, SI method can be
effectively used to determine the parameters of a fully developed vehicle. This approach pro-
vides the dynamic model with the high degree of fidelity since the experimental data utilised
Chapter 7. Control Application
126
for modelling are acquired under real operational conditions. Also, the variation of the hydro-
dynamic coefficients due to changes in the external configuration of a modular underwater ve-
hicle in a specific mission (for example, in a case of adding an extra payload module to the base
vehicle configuration of the vehicle) can be rapidly determined using SI. For that reason, the SI
approach is versatile and cost effective. However, there are some practical concerns associated
with performing system identification on AUVs. The first is that the experimental data were
collected in the presence of noise and turbulence. Despite relatively calm wind and water con-
ditions at test site, there are external influences to a certain degree. The noise could result in an
increased variance in the least squares parameter estimation. Therefore the SI approach requires
the physical system to be sufficiently instrumented in order to accurately measure the necessary
state variables with minimum noise effects. The second issue is the estimation of mathematical
model relied on the data collected from close-loop feedback control system which may cause
the immeasurable noise to be correlated with the input (Ljung, 1998).
In the literature, there have been a wide range of SI algorithms developed for the underwater
vehicle, including Least Squares (LS), Extended Kalman filter (Kim et al., 2002; Sabet et al., 2014),
Maximum Likelihood and Neural Network (Badillo and Ceron; Shafiei and Binazadeh, 2015)
for both offline and online applications. These methods generally minimises the errors between
vehicle state variables predicted by the dynamic model and actual measured state variables. A
compromise between complication and accuracy was considered to determine an appropriate
method for the study. Since the underwater vehicle nonlinear dynamic equations of motion can
be expressed in state space models linearized in the range of the cruising conditions, the LS
algorithm is prevalent and effective for the practical system identification. It is able to be derived
in the offline condition, the Ordinary or Weighted Least Squares, and in the online condition,
the Recursive Least Squares. While there has been a significant amount of published works on
LS technique for open frame ROVs (Avila et al., 2013; Martin and Whitcomb, 2014; Weiss and
Chapter 7. Control Application
127
Du Toit, 2013; Xu et al., 2015; Avila et al., 2008), studies for torpedo-shaped AUVs are limited,
which are carried out in horizontal plane for steering subsystem (Hegrenaes et al., 2007; Eng et
al., 2016) and vertical plane for diving subsystem respectively (Petrich et al., 2007) .
This thesis utilises the offline LS algorithm to derive an experimentally validated state space
model that is able to describe the manoeuvring characteristics of a torpedo shaped AUV for both
steering and diving subsystems. The experimental data used for the system identification study
are acquired from the on-board sensors during the field trails. The proposed SI approach con-
sists of two stages, which are comprehensively described in the next sections. Instead of esti-
mating the hydrodynamic coefficients and predicting the system response based on the state
variables in a given time period, the simulator with optimised hydrodynamic coefficients re-
sulted from the proposed procedure is able to simulate system response from specific initial
conditions in the time domain to meet the desired requirements. This approach is slightly dif-
ferent from previous studies on system identification of underwater vehicle and it is the main
contribution of this section.
7.1.2 Linear Mathematical Model
There is a large number of linear as well as nonlinear hydrodynamic derivatives presented in
the 6-DOF mathematical model of the AUV. Therefore, the identification of the complete set of
coefficients is rather complex task. That is the reason why the assumptions should be made to
simplify it. A widely used approximation can be achieved if it is assumed that the hydrodynamic
force function , , tf ν θ consists of the linear drag forces only, the hydrostatic force function
, , tg ν θ consists of the buoyancy forces only and if the inertia matrix including the added
mass is time-space invariant and diagonal (Tiano et al., 2007).
Chapter 7. Control Application
128
The complete 6-DOF can be decomposed into three essentially non-interacting subsystems con-
stituted by (a) the lateral subsystem, (b) the longitudinal subsystem and (c) the speed subsystem.
These subsystems combined will provide an overall picture of the hydrodynamics of the AUV.
This traditional approach is applicable in practice for streamlined torpedo-shaped AUVs when
the coupling between subsystems is weak and may be reasonably neglected without serious loss
of information (Hong et al., 2013; Caccia et al., 2000). In this work, the lateral subsystem and
longitudinal subsystem are of specific interest.
The additional assumptions in the horizontal plane (x-y plane) and the vertical plane (x-z plane)
for decoupled subsystems respectively are given in Table 7.1 as follows (Hong et al., 2013;
Jalving, 1994):
Table 7.1. Assumptions in horizontal and vertical planes.
Horizontal plane
(Lateral subsystem)
Vertical plane
(Diving subsystem)
Heave velocity 0w Sway velocity 0v
Roll angle 0 Roll angle 0
Pitch angle constant, 0 Yaw angle constant, 0
For small roll and pitch angles,
sin cos
cos cosq r r
For small pitch angle, q
Finally, under the assumption of constant forward speed 0
u U , a corresponding set of linear-
ized time-invariant models are derived in horizontal plane and vertical plane respectively are
presented as follows:
Chapter 7. Control Application
129
The lateral subsystem:
1 2 3 41 2 3 4
0 0
0 1 1 0 0 0 0 0zz r r
I N r N r N N N N
(7.1)
The longitudinal subsystem:
11 2 3 4
2
30
4
0 0 0
0 1 0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0
yy q q zI M M BG Wq q M M M M
z U z
(7.2)
where ,yy zz
I I are the moment of inertia, z
BG is the distance between the centre of gravity and
the centre of buoyancy; , , , , ,ir r i q q
N N N M M M
are the hydrodynamic derivatives. They are the
partial derivatives of the forces and moments with respect to the corresponding accelerations,
velocities or control surface deflection, e.g. :r
NN
r
Equation (7.1) and (7.2) are presented in state space model for computational convenience below:
1
21 1 2 3 4
3
4
0
1 0 0 0 0 0
r a r b b b b
(7.3)
where 1
r
zz r
Na
I N
11 2 1 2 3 4
2
30
4
0
1 0 0 0 0 0 0
0 0 0 0 0 0
q c c q d d d d
z U z
(7.4)
where 1
q
yy q
Mc
I M
,
2z
yy q
BG Wc
I M
, i
i
yy q
Md
I M
Chapter 7. Control Application
130
Rewriting equation (7.3) and (7.4) with the focus on equations which include parameters to be
estimated:
1
1
1 2 3 4 2
3
4
a
b
r r b
b
b
(7.5)
1
2
11 2 3 4
2
3
4
c
c
dq q
d
d
d
(7.6)
Due to Gavia’s unique control surface configuration, input signals consist of four independent
values i in degree respectively. In previous works (Hong et al., 2013; Petrich et al., 2007) , there
was only one input signal for each subsystem; i.e., elevator input signal for diving subsystem
and rudder input signal for steering subsystem. In the state space equations in both steering and
diving subsystems, , , ,i i i i
a b c d are the model parameters, which consist of physical parameters
and hydrodynamic coefficients sufficiently describing the system characteristics. It is important
to note that the hydrodynamic coefficients are not determined specifically but this does not af-
fect the applicability of identified model. The following section describes the identification pro-
cedure and least squares algorithm implemented to identify , , , .i i i i
a b c d
7.1.3 Identification Procedure and Least Squares Method
7.1.3.1 Proposed identification procedure
Figure 7.1 outlines the proposed system identification procedure based on reference (Klein and
Morelli, 2006).
Chapter 7. Control Application
131
Within the previous section, the mathematical model of the AUV was developed using prior
model postulation about hydrodynamic characteristics of underwater vehicles. Field experi-
ments were then carried out with the AUV and the collected data were analysed for parameter
estimation. In the stage one of the two-stage identification process, the least squares algorithm
was utilised to identify the estimated parameters for the previously developed mathematical
model.
Figure 7.1. Summary of the proposed identification procedure.
The goal was to find a set of parameter iθ that minimises the average residual error
(Chirarattananon and Wood, 2013):
Chapter 7. Control Application
132
measurement prediction
i
d dr
dt dt
i iX X (7.7)
where 1
rX , 1 1 1 2 3 4
Ta b b b b θ in equation (7.5)
2qX , 2 1 2 1 2 3 4
Tc c d d d d θ in equation (7.6)
Model verification was also executed for different sets of data to verify the identified model. At
this stage, the identified model was only able to predict the system response ,r q from given
current measured states , ,r q for a certain period of time. The principal goal of the study was
to develop the desired simulator which could capture the accurate response of vehicle for a long
term behaviour from a given initial condition. Motivated by these references in the unmanned
aerial vehicle field (Hoburg and Tedrake, 2009; Chirarattananon and Wood, 2013), the next op-
timisation process was considered in stage two to determine an updated set of parameter iθ
that minimise the error i
e between the measured output signal and simulated output signal
computed by simulating the identified model from specified initial condition with similar con-
trol input signals:
measurement simulationie
i iX X (7.8)
where simulationi
X is obtained by simulating equation (7.5) and (7.6) with initial set of parameter
iθ .
The final results were the updated values of parameter iθ . Both minimisation processes for
equation (7.7) and (7.8) were based on the least squares algorithm which is presented in the
following section.
Chapter 7. Control Application
133
7.1.3.2 Least Squares Optimisation algorithm
Using the matrix notations, the dynamic equations (7.5) and (7.6) can be written in the form of
equation (7.9)
y = Hθ (7.9)
where H is the measured state and control input vector
y is the estimated output vector
The measured output vector z of y is defined
z Hθ ε (7.10)
where ε is the vector of random measurement errors and assumed to be zero mean and uncor-
related with constant variance.
The Ordinary Least Square (OLS) identification method is based on the Equation Error Method.
According to this, the identification of parameter vector θ is equivalent to the minimization of a
scalar cost function (Klein and Morelli, 2006; Ljung, 1998):
21 1
2 2 2J θ ε z Hθ (7.11)
Solving equation 0
J
θ for the unknown parameter vector θ gives the formula for the OLS
estimator,
-1
T Tθ H H H z (7.12)
In practical cases, the assumptions of uncorrelated measurement errors and homogeneous var-
iance are not valid (Klein and Morelli, 2006). The noise covariance matrix V is introduced and
the formula for Weighted Least Squares (WLS) estimator,
Chapter 7. Control Application
134
-1
T -1 T -1θ H V H H V z (7.13)
To validate the result of estimator, the Mean Squares Error (MSE) 2 can be estimated (Klein
and Morelli, 2006):
2
2
1
1 N
i
i iN
z z (7.14)
7.1.4 Experimental Setup and Data Processing
A series of trials with Gavia AUV were conducted in May 2015 at Trevallyn Lake, Tasmania,
Australia as shown in Figure 7.2. The tests were conducted in relatively calm wind and current
conditions. In order to identifying the hydrodynamic coefficients of the two subsystems, the free
running tests in both longitudinal and lateral subsystem were performed separately to fully ex-
cite the dynamic models of AUV system. It is important to design the missions that covers the
total operational range.
During the experiments, the vehicle was controlled to cruise in certain design manoeuvre. For
experiments in vertical plane, the AUV was continuously changing depth in the range of 0 – 5
m while maintaining constant heading. On the other hand, for experiments in horizontal plane,
it was controlled to perform turning manoeuvers while keeping constant depth. The control
surface angles varied from -20 to 20 degree. During all experiments, the AUV was commanded
to track predefined waypoints with a constant forward speed at 1.6 m/s.
Chapter 7. Control Application
135
Figure 7.2. Experimental location (Tran et al., 2015a).
Figure 7.3. Gavia AUV performing designed manoeuvrability.
The Gavia AUV was instrumented to measure the necessary state variables. It used the Kearfott
T-24 integrated seaborne navigation system combined with a Kalman filter. The INS provided
accurate linear and angular accelerations, the Doppler Velocity Log (DVL) provided velocity
(b)
Trevallyn Lake
(b)
(a)
N
Tasmania
Australia
Chapter 7. Control Application
136
(Hiller et al., 2011). The acceleration data were obtained and used as input to the SI process by
numerical differentiation of gyro data in the case that the efficient acceleration sensors were not
available (Hong et al., 2013; Petrich et al., 2007). 3DM-GX1 Gyro Enhanced Orientation Sensor
supplied additional information about the angular velocity and orientation. Since there are no
integrated sensors to measure the actual control surface angles, the commanded angles sent by
the autopilot system were used. The measured trial dynamic data obtained by the on-board
sensors. Prior to applying SI procedure, these data from were resampled to form an integrated
set of data since the sensors had different sampling rates.
7.1.5 Results and Discussion
7.1.5.1 Stage one – Identifying the model
After pre-processing data from system files, previously described methods were applied to iden-
tify the parameters for both lateral and longitudinal subsystems of the Gavia AUV dynamic
model. In the stage one, the initial goal was to fit the experimental measured angular accelera-
tion data to the predicted data. Four segments of experimental data were utilised in these stages
for lateral and longitudinal subsystem identification respectively.
The comparison between the measured data and the predicted results of the angular accelera-
tion calculated in stage one is illustrated in Figure 7.4 and Figure 7.5. As can be seen, the data
from predicted models are generally in good fit with the measured data as expected. The mean
square errors are 2 4
11.92 10 for r (rrate) data and 2 4
21.94 10 for q (qrate) data. There
are overshoots and undershoots at some points. This might be a consequence of fast response of
physical system in which angular velocity and acceleration could not be captured accurately by
sensors. In addition, angular velocity and acceleration data were recorded by two sensors sepa-
rately (Gyro and INS).
Chapter 7. Control Application
137
Figure 7.4. Comparison between the predicted (solid line) and measured (dash lines) angu-
lar accelerations for lateral subsystem.
Figure 7.5. Comparison between the predicted (solid lines) and measured (dash lines) angu-
lar accelerations for longitudinal subsystem.
Chapter 7. Control Application
138
Figure 7.6. Comparison between the predicted (solid lines) and measured (dash lines) yaw
angular acceleration for the lateral subsystem.
Figure 7.7. Comparison between the predicted (solid lines) and measured (dash lines) pitch
angular accelerations for the longitudinal subsystem.
Chapter 7. Control Application
139
A new set of experimental data, different from the data used in the previous stage, was applied
to verify the fidelity of estimated parameter. This validation process is essential in SI to check
whether or not the model identified from a particular experimental data is applicable under
different operational conditions.
In the comparison shown in Figure 7.6 and Figure 7.7 it can be seen that the predicted angular
acceleration responses fit closely to the measured data in both lateral and longitudinal subsys-
tems. Their magnitudes and trends over time are mostly coincidental. From the results obtained
in the stage one of the SI and in the validation process, it can be concluded that the identified
model are able to accurately predict the system response from given vehicle state’s values.
7.1.5.2 Stage two – Optimising the model
The obtained identified model was sufficiently effective in predicting the system responses for
a certain time period or for a combination of different set of data. It means that the identified
model up to this stage only demonstrates the vehicle hydrodynamic characteristics in a specific
condition at which the experimental data were collected. However, in order to develop a robust
simulator to accurately predicting the response in a long term behaviour from a given initial
condition, in the stage two the identified model was optimised by fitting the experimental data
to the simulated data generating from numerical simulator in the stage one. The initial condition
was selected equally to the first state value in the set of experimental data used as inputs for
simulation validation. Numerical simulations in the time domain were performed based on the
optimised model by using the Fourth Order Runge-Kutta ODE integration algorithm.
In Figure 7.8 and Figure 7.9, the numerical simulation results of optimised model for angular
acceleration are compared to the actual measured results for a set of experimental data in the
lateral and longitudinal systems.
Chapter 7. Control Application
140
Figure 7.8. Comparison between the simulated (solid lines) and measured (dash lines) angu-
lar velocity yawrate for lateral subsystem.
Figure 7.9. Comparison between the simulated (solid lines) and measured (dash lines) an-
gular velocity pitchrate for the longitudinal subsystem
Chapter 7. Control Application
141
In the lateral subsystem, it is noted in Figure 7.8 that the optimised model is able to represent
appropriate tendency and frequency response compared to the measured response for the
yawrate. Nevertheless, the comparison shows that there is a small offset and oscillation between
the simulated and measured data, their amplitudes are not consistent. This is probably due to
the variation in the forward speed of the vehicle during manoeuvres since the controller contin-
uously changes the propeller rotational speed to compensate for the thrust loss during the turn-
ing manoeuvre in horizontal plane. The assumption of constant forward speed is valid in the
simulation, whereas there is a slight difference in practice.
It is seen from Figure 7.9 that in the longitudinal system, the pitchrate response from the simu-
lation program demonstrates a good agreement with the measured data. However, there are
some overshoots during pitch motion that the simulated data do not fit closely with the experi-
mental data. The differences in their responses at the peaks are mainly due to the control surface
saturation in practice during the manoeuvres in which the vehicle performs the continuous
pitching and diving motion. Additionally, the minor environmental disturbances occurring in
the field trials might result in the variation between the simulated and measured data in both
model. In essence, two optimised models for lateral and longitudinal subsystems derived fol-
lowing the two-stage SI procedure are able to reasonably predict the responses of the torpedo
shaped underwater vehicle in a given initial condition. The parameters obtained from the LS
optimised model are summarised in Table 7.2.
Furthermore, based on these parameters, the analysis could be performed to evaluate the stabil-
ity of the vehicle. The negative value of 1
a and 1
c shows that the yaw dynamics and pitch dy-
namics are stable (Hong et al., 2013). It is worth noting that the absolute values of four control
surface hydrodynamic parameters i
b and i
d are identical in each subsystem. The sign differ-
ence is resulted from the definition of rotational direction for each control surface.
Chapter 7. Control Application
142
Table 7.2. Identified parameters for longitudinal and diving subsystems
Lateral Subsystem Longitudinal Subsystem
Parameter Value Parameter Value
1a -0.9497 1
c -0.9093
1b 0.00062 2
c -0.0094
2b -0.00062 1
d -0.006
3b 0.00062 2
d 0.006
4b -0.00062 3
d 0.006
4d -0.006
In addition, the eigenvalues of equations of motion are also utilised to determine the stability
and response of the system. From the obtained values of the parameters 1 1 2, ,a c c , the stability of
yaw and pitch dynamics are able to be analysed based on the stability conditions of linear state
space model.
From equation (5) the eigenvalues of the matrix 10 0.9497 0
1 0 1 0
aA
are 1
0.9497A
and2
0A . Since
10
A and
20
A the yaw dynamic of AUV is stable.
From equation (6) the eigenvalues of matrix 1 2
0
0 0.9093 0.0094 0
1 0 0 1 0 0
0 0 0 1.6 0
c c
B
U
are
10
B ,
20.0105
B and
30.8988.
B Since
1 2 3, , 0
B B B the pitch dynamic of AUV is sta-
ble.
Chapter 7. Control Application
143
7.1.6 Summary
In this section, the two-stage system identification based on least squares algorithm is developed
to estimate reasonably the underwater vehicle linear mathematical model. The experimental
data used for the system identification study were acquired from the on-board sensors during
the field trails. The model parameters are identified and optimised. The obtained results have
proved the effectiveness of the proposed two-stage SI in determining the linear hydrodynamic
coefficients of a torpedo-shaped underwater vehicle. In the next section, the linear control design
based on the developed linear mathematical model is presented.
7.2 Control Application
7.2.1 Introduction
The optimal control design presented in this section is a part of the research project to examine
the control of an AUV equipped with CCPP at both cruising speed and low speed in a typical
surveying mission.
The system modelling and control design for underwater vehicle are challenging and compli-
cated in practice due to the nonlinear behaviour of underwater vehicles and the external dis-
turbance of operating environments. The wide range of applications and AUV configuration has
resulted in the development of control system with various control strategies. There are three
typical types of controller for marine robotics including the classical feedback control, the mod-
ern feedback control and the advanced nonlinear control. A number of commonly used control
algorithms for AUV are the Proportional Integral Derivative controller (PID) (Taubert et al.,
2014), H-infinity controller (Wang et al., 2015), neural network (van de Ven et al., 2005), sliding
mode control (SMC) (Londhe et al., 2016), fuzzy logic (Ishaque et al., 2011), adaptive control
technique (Hassanein et al., 2016) and the linear quadratic regulator (LQR). After considering
Chapter 7. Control Application
144
the control strategy of various AUVs, the optimal LQR algorithm is considered in this study due
to its reliability, computationally inexpensive, and ease of implementation in the primary design
stage. LQR is a commonly used controller and has been applied successfully in various autono-
mous systems such as unmanned aerial vehicles (Bouabdallah et al., 2004), and unmanned sur-
face vessel (Naeem et al., 2008). In addition, as compared to the classic control method such as
PID, the modern control method LQR has several advantages such as stability and non-sensitiv-
ity to the dynamic model. The LQR controller could handle the model uncertainty, sensor noise
and environmental disturbance better than the PID controller could.
The design of LQR for AUV equipped with CCPP is based on the assumption that the vehicle
dynamics can be decoupled to the linear longitudinal and lateral subsystem. In this study, two
separate LQR controllers for the depth and heading control are presented.
The following sections describe the optimal LQR algorithm; derive the control objective for the
study; and perform the simulation of proposed LQR for depth and heading control.
7.2.2 Control Algorithm
Much of the controller design for AUV system in practical operation uses linear control methods,
based on either the simplified linear models, or the linearisations of the nonlinear model. The
effectiveness of the linear controller such as optimal control method on the AUV with CCPP is
yet to be demonstrated in literature. In this section, the closed-loop optimal control for AUV is
addressed.
7.2.2.1 Linear Quadratic Regulator
The general 6 DOF model of an AUV involves highly nonlinear and coupled equations that re-
sults in the high complexity in the model based controller. Therefore, in the common practice of
Chapter 7. Control Application
145
control design, the general motion equations can be decomposed into three subsystems to de-
scribe the hydrodynamics of an AUV: the lateral subsystem, the longitudinal subsystem, and
the speed subsystem. In this study, the focus is on the longitudinal and lateral subsystems. This
traditional approach is applicable in practice for streamlined torpedo-shaped AUVs to reduce
the complexity when the coupling between subsystems is weak (Eng et al., 2016).
In addition, the nonlinear dynamic model of the AUV was linearized at certain equilibrium con-
ditions in order to apply the linear LQR controller. The equilibrium conditions were investigated
at which the AUV cruising speed was 1.5 m/s and the other translational velocities are zero. The
state space models for lateral and longitudinal subsystems are presented as (Tran et al., 2015a):
1 0
1 0 0cyc
r a r
(7.15)
1 2
0
0
1 0 0 0
0 0 0
cyc
q b b q
z U z
(7.16)
where 1,a
1,b
2b are the model hydrodynamic coefficients derived by using the system identi-
fication method (Tran et al., 2015a) and verified by the analytical method. , are the propul-
sion model coefficients estimated from previous sections.
This section presents the optimal state feedback controller using LQR technique. The LQR tech-
nique is a class of modern feedback control method. The controller is used to control the hori-
zontal and vertical movements separately at equilibrium conditions. Equation (7.15) and equa-
tion (7.16) can be expressed in the general state space form:
x = Ax +Bu
y = Cx +Du (7.13)
Chapter 7. Control Application
146
The LQR design problem is to calculate the state feedback controller K such that the objective
quadratic function J is minimised (Antsaklis and Michel, 2007):
0
J dt
T Tx Qx + u Ru (7.14)
Where Q and R are the state and control penalty matrices. They are defined and selected to
ensure accurate dynamics of the system.
The applied control law is given as:
u K x (7.15)
where x is the error in the outputs that are controlled and u is the control signals.
The constant K is obtained:
-1 TK = R B P (7.16)
P is determined by solving the Riccatti equation (Lewis et al., 2012):
T -1 TA P+PA-PBR B P+Q= 0 (7.17)
7.2.2.2 Control Objective
One of the typical missions of surveying style AUV is conducting a survey with the lawn mower
pattern while maintaining a desired depth over the bottom. This mission is practically con-
ducted in several applications including oceanographic research, biological sampling, and mine-
sweeping. The surveying mission is selected as the case study for the controller design of the
AUV equipped with CCPP in which the heading and depth control are considered. These two
control tasks are one of the most popular control modes in the control study of an unmanned
underwater vehicle. The simulation is conducted to demonstrate the feasibility of the design
control law.
Chapter 7. Control Application
147
Figure 7.10. The lawn mower pattern.
During this mission, the control objective was to control the AUV at desired depth and heading
values by adjusting the input cyclic angle .cyc
cyc was limited to 20 degree for the control de-
sign. It was also assumed that the AUV forward speed is constant in these operating conditions
and the state initial values were zero. The performance requirement for the system under control
was minor oscillation about the reference input signals.
7.2.3 Simulation Results
The AUV dynamic model and LQR controller are implemented in the simulator using
MATLAB/SimulinkTM. The Runge-Kutta fourth order solver are utilised. The simulation aims to
demonstrate the performance of the AUV equipped with CCPP in the time domain. The full
state feedback is assumed for the controller. The AUV depth and heading control problem are
conducted and examined separately.
Chapter 7. Control Application
148
7.2.3.1 Depth Control
In the proposed manoeuvre for the depth control problem, the AUV was controlled to maintain
the desired depth of 18 m and then 3 m after 80 s. The simulation time was 125 s.
Figure 7.11, Figure 7.12, and Figure 7.13 show the depth, pitch angle and control input signal as
the function of time respectively. As can be seen, the depth variable is successfully controlled
with minor overshoot. After a short period, the depth value converges to the first reference input
value. The setting time is approximately 22 s. This value is reasonable considering that the AUV
is in the low speed operation. The simulation also shows a decrease in depth as the controller
acquire a second reference input. The AUV is therefore able to track the continuous reference
input signals.
Figure 7.11. Depth control using the LQR.
Chapter 7. Control Application
149
Figure 7.12. Pitch angle variation in the depth control.
Figure 7.13. Input cyclic angle of the CCPP.
Chapter 7. Control Application
150
7.2.3.2 Heading Control
Similarly, the performance of the heading control system using LQR is presented. The simulated
scenario for the heading control was that the AUV needs to change the yaw angle to 0.8 rad and
then to -0.3 rad after 30 s. The total simulation time was 60 s.
Figure 7.14 shows the response of yaw angle in the lateral plane and Figure 7.15 shows the cor-
responding control signal as the function of time. It can be seen from the simulation that the
AUV is able to maintain the desired heading with no overshoot and the CCPP works effectively.
The cyclic angle is adjusted to its maximum value and then gradually to its initial position.
Figure 7.14. Heading control using the LQR.
Chapter 7. Control Application
151
Figure 7.15. Input cyclic angle of the CCPP.
7.3 Summary
The goal of this chapter was to accurately control the depth and heading of an AUV equipped
with CCPP. In the study, the Gavia AUV was used as the research platform to implement the
designed controller. In the first section, the two-stage system identification based on least
squares algorithm was developed to estimate reasonably the underwater vehicle linear mathe-
matical model. The experimental data used for the system identification study were acquired
from the on-board sensors during the field trails. The time-domain validation test showed that
the proposed two-stage SI approach delivered a high-fidelity dynamic model. In the second sec-
tion, the LQR algorithm was implemented for the control design of an AUV equipped with
CCPP. Two separate LQR controllers were designed for the longitudinal and lateral subsystems.
The effectiveness of the proposed controllers was analysed by using the numerical simulation
approach. As could be seen on the simulation results, the heading control behaved as good as
the depth control. The AUV performance with CCPP under LQR controller demonstrated that
Chapter 7. Control Application
152
the linearised dynamic model was suitable for the application of the optimal control. The steady
state response of the system such as overshoot and settling time met the performance require-
ments.
153
CHAPTER 8
CONCLUSIONS AND FUTURE WORK
This thesis focused on the analysis of the CCPP propulsion system in order to improve the un-
derwater vehicle performance and manoeuvrability with respect to the conventional FPP system.
The experimental and simulation studies presented in the previous chapters gave valuable in-
sights into the performance characteristics of the CCPP propulsion system and the AUV
equipped with CCPP. In the final chapter, the results of the research project are summarised,
including the completed works, main findings, conclusions, and the significance of the research
project. The potential avenues for future work are also illustrated.
Chapter 8. Conclusions and Future Work
154
8.1 Summary of the Completed Works
The use of CCPP as the propulsion system for a torpedo-shaped AUV represents a novel and
challenging problem and is the main motivation for the research project. This thesis presents the
performance analysis of the innovative CCPP propulsion and a comparison study of two pro-
pulsion systems named FPP and CCPP as applied to the Gavia AUV. A considerable amount of
significant tasks was conducted during the course of the research project and are summarised
in this section.
For the purpose of improving the manoeuvrability of AUVs at low speeds, the need for an in-
novative propulsion system was addressed. A variety of state of the art propulsion systems for
an underwater vehicle were described and analysed. A comprehensive literature study was
mentioned to describe the relevant propulsion systems with different configurations as alterna-
tive propulsion system to the conventional one. A brief description and performance analysis of
these propulsion systems were conducted, discussing the advantages and disadvantages of us-
ing these systems.
The process of developing the AUV’s equations of motion that can effectively model the vehi-
cle’s behaviour and performance characteristics was illustrated. The derivation of the six DOF
nonlinear equations for an AUV was considered. The six degree of freedom equations of motion
for underwater vehicle simulation are general sufficient to simulate the trajectories and re-
sponses of the submarine resulting from normal manoeuvres as well as for extreme manoeuvres
(Gertler and Hagen, 1967). The hydrodynamic coefficients are the sensitive parameters to the
AUV performance in the simulation. In this stage, the experimental study of Gavia AUV in the
Towing Tank has not been conducted to determine its hydrodynamic coefficients. Therefore, in
the scope of this project, the hydrodynamic coefficients were mainly estimated based on the
Chapter 8. Conclusions and Future Work
155
analytical approaches that represent a reasonable trade-off in terms of accuracy and ease of im-
plementation. The asymmetric shape of Gavia AUV helps to reduce the hydrodynamic com-
plexity in the modelling process. These coefficients were validated and verified to minimise the
uncertainty in the calculations. The obtained results were adjusted considering the data from
the previous studies in the literature.
There has been extensive experimental work conducted to increase the knowledge of the prin-
ciples and characteristics of the conventional FPP propulsion and CCPP propulsion system. The
propulsion systems have the high level of effects on the AUV behaviour and the study on their
performance is critical. The new modelling of the FPP and CCPP propulsion system character-
istics was developed using the experimental approach. The accurate modelling of the propul-
sion system paves the way for development of the simulation and control study. The fundamen-
tal objective of these two chapters was to measure the thrust and manoeuvring forces generates
from these two propulsion systems. The sensitivity analysis based on the obtained test data pro-
vided the validity of the experimental results. The experimental procedure and data analysis
were mainly based on the ITTC standard for marine propulsion testing. The experimental data
were then applied to derive the propulsion system empirical model incorporated in the numer-
ical simulation program.
A simulator for an underwater vehicle named AUVSIPRO was constructed in
MATLAB/SimulinkTM platform. AUVSIPRO was a part of a research project to examine the ap-
plicability of the FPP and CCPP to an AUV. This program was developed with the emphasis on
the performance prediction of an underwater vehicles equipped with different propulsion sys-
tems in the early design stage. The AUVSIPRO could also be extended to adapt to a variety of
underwater vehicles and propulsion systems, for example the Mullaya AUV and Explorer class
AUV at AMC-UTAS. A model predicting the manoeuvring forces generated by the FPP and
Chapter 8. Conclusions and Future Work
156
CCPP propulsion system was applied to AUSIPRO. The forces and moments generated by the
propulsion systems were mapped to the dynamics of the AUV to form the complete model. This
method provided advantages of comprehensive formulation and rapid computation.
The controller design for an AUV equipped with CCPP was developed to guarantee the system
robustness against external disturbances in operation. The two-stage identification method to
define the linear model of Gavia AUV and the optimal control development were analysed. The
depth and heading control was conducted to validate the controller. The performance of the
proposed controller was demonstrated and verified by simulation. This controller was compu-
tationally inexpensive and effective in application.
8.2 Main Findings and Conclusions
The experiment of an FPP for Gavia AUV was tested at the towing tank in all four quadrants of
operation. The conventional open water performance in the first quadrant and the performance
characteristic in four-quadrant operation are presented in this study. An analysis of using poly-
nomial and Fourier series regression model in representing the experimental data sets is exam-
ined. It is concluded that the four-term and three-term Fourier series regression models are con-
sidered the most appropriate models in representing the thrust and torque coefficient curves
respectively in the specified condition of this study. These two models form the four-quadrant
underwater propeller model. They are able to produce a reasonable approximation of thrust and
torque coefficients with a small number of parameters.
Although the initial experiments of CCPP prototype were conducted in previous studies, this
investigation has provided a systematic experimental data on the CCPP performance. The im-
provements were made to the experimental system and data collection. A series of comprehen-
sive bollard pull and captive model tests were designed and conducted on the innovative pro-
pulsor CCPP to evaluate its performance. The effects of the collective and cyclic pitch settings
Chapter 8. Conclusions and Future Work
157
on the CCPP performance have been examined and discussed. According to the obtained results,
it was shown that the CCPP was capable of generating effective manoeuvring forces in both
bollard pull and captive model conditions. The results also provide an insight into the relation-
ship between these manoeuvring forces and controlled parameters that enable the simulation
and control study of the underwater vehicle equipped with CCPP. The dynamic modelling of
the propulsion systems using the experimental approach is reliable and integrated in the entire
AUV dynamic model to create a realistic simulation.
The proposed simulation program proved to be quite effective and feasible in describing the
manoeuvring capabilities of an AUV equipped with these two examined propulsion system.
The standard manoeuvring tests for marine vehicles were presented for the investigation about
the influences of conventional FPP and CCPP propulsion on the Gavia AUV. The simulation
results indicate that the AUV equipped with CCPP provides better manoeuvrability in compar-
ison to the AUV equipped with conventional FPP propulsion system. In the considered manoeu-
vring tests, the CCPP outperforms the FPP in most of the examined parameters and variables.
Five separate fundamental manoeuvring tests are presented to demonstrate the performance
differences between the two configurations. The simulation program presented the obtained re-
sults, which were consistent with the expected behaviours of the two propulsion configurations.
In the acceleration test, the results indicated that the CCPP propulsion has an advantage for high
acceleration rate; meanwhile the conventional FPP propulsion is beneficial better steady forward
speed. In the static turning manoeuvre and zigzag test, there is a clear advantage with respect
to the CCPP configuration in terms of heading changing ability. The shorter stopping distance
and time are due to the faster deceleration rate in the stopping test show the better stopping
performance of CCPP. The simulation results also reveal that the CCPP has the superior diving
characteristic in the vertical plane. In conclusion, with respect to the primary manoeuvres rep-
Chapter 8. Conclusions and Future Work
158
resenting the operation of an AUV, the CCPP propulsion system has better performance charac-
teristic, which allows for precise surveying tasks. Furthermore, it is proved that the CCPP is
capable of providing low enough continuous thrust to enable the low speeds desirable for accu-
rate manoeuvring and inspection tasks. It could be concluded that the CCPP provides the ma-
noeuvrability to a greater degree and this is the most important aspect considered in this thesis.
This type of propulsion system is feasible and it is one of the viable alternatives to the conven-
tional FPP configuration in an AUV, especially in the low speed operation. It also be noted that
the CCPP selection does not represent the best trade-off in every situation.
The other important feature concerning the application of a newly developed propulsion system
for an AUV is its accurate operation under the controller. The CCPP is able to provide control
authorities independent of the relative flow as compared to the conventional FPP with control
surfaces. The new two-stage system identification based on least squares algorithm was devel-
oped with the goal of estimating reasonably the Gavia AUV linear mathematical model. The
experimental data used for the system identification study were acquired from the on-board
sensors during the field trials. This methodology is considered as a general tool that could be
reused for design and evaluation of different systems. The LQR algorithm was implemented for
the control design of an AUV equipped with CCPP. Two separate LQR controllers were de-
signed for the longitudinal and lateral subsystems. The effectiveness of the proposed controllers
was analysed by using the numerical simulation approach. The integrated simulation and de-
sign framework facilitate the development and testing of the controllers. From the simulation
results, the heading control behaved as good as the depth control. The optimal controller pro-
vided the desired accuracy in both heading and depth control in which there were smooth tran-
sitions between different operating conditions in low speed performance. The AUV perfor-
mance with CCPP under LQR controller has demonstrated that the developed dynamic model
is suitable for the application of the optimal control. The obtained results enable a good basis
Chapter 8. Conclusions and Future Work
159
for the future controller design as the proposed control strategy is applied to the realistic vehicle
to enhance its autonomy.
8.3 Significance of the Research
The new applications of marine science and engineering require the underwater vehicle with
high autonomy, excellent performance characteristic, and precise manoeuvrability. These as-
pects are highly subject to the propulsion system. The primary content of this thesis is about the
performance characteristic of an underwater vehicle equipped with the novel CCPP propulsion
system and its manoeuvring comparison to the conventional FPP propulsion. The ultimate ob-
jective of the thesis is to investigate the feasibility of the CCPP as the propulsion system of choice
for a torpedo shaped underwater vehicle instead of the conventional FPP with control surfaces.
This research effort has provided the contributions to the field of underwater robotics.
The research and development of a new AUV is both complex and expensive, especially for the
AUV equipped with a new propulsion system. The greatest difficulty lays in characterizing its
system performance. In current research, the analytical approach, experimental method and nu-
merical simulation are utilised to validate the performance of an AUV in the preliminary devel-
opment stage. The proposed methods and procedures are presented in a systematic process and
they are applicable to any changes of the system design, as well as to other systems of similar
characteristics. Time and money can be saved by using a systematic approach when the new
designs are frequently updated. The unified simulation model based on the experimental data
provides researchers with the ability to test new designs or any modifications to existing ones
in a simulation environment. The developed AUVSIPRO simulator could be easily extended to
different propulsion system and to various underwater vehicle configurations. It provides a use-
ful means to verify the system and the software design before implementing on the hardware
platform.
Chapter 8. Conclusions and Future Work
160
In conclusion, the main finding highlights and proves the superior manoeuvrability and relia-
bility of the CCPP propulsion system with respect to the conventional FPP configuration. The
considerable advantages of CCPP propulsion in performance are confirmed in the study using
experimental and simulation approach. The successful implementation of the optimal control
strategy on the AUV with the CCPP propulsion system is also considered as a significant aspect
of the overall contribution. The analysis presented in this thesis can serve as a proof-of-concept
for the research of underwater propulsion system. It is concluded that the CCPP propulsion
system is an excellent alternative propulsion to the conventional FPP for an AUV, especially in
the operations that require the combination of both high-speed surveying and low-speed ma-
noeuvrability.
8.4 Future Research
In the course of this thesis, although a considerable number of tasks has been accomplished
some works could not be completely conducted in the given timeframe. This section will high-
light some of the works, which require additional thorough research and investigation for the
more accurate results. Moreover, the suggestions and recommendations for the future study are
also presented.
In the context of this project, the interactions between the CCPP propulsion system and the AUV
hull have not been examined in term of hydrodynamics. It is assumed that this interaction has
the minor contribution to the total forces. However, the knowledge about this issue would pave
way for the optimisation of the CCPP blade design and the improvement of the manoeuvring
performance simulation. Additionally, the simulations have taken into consideration the inter-
action effects between the collective and cyclic pitch settings by using the empirical model from
the tests. The hydrodynamic investigation on their performance characteristic has not been con-
sidered in the experimental approach. These issues have been addressed with the use of CFD
Chapter 8. Conclusions and Future Work
161
approach in the works of other PhD student at AMC. The stabilisation analysis of the CCPP
could be conducted from the study of this interaction.
Since the CCPP propulsion is characterised by a high manoeuvrability at low speed, the cavita-
tion would be an interesting issue to examine. The study of cavitation will demonstrate the lim-
itation in the operational range of an AUV with CCPP. Hence, the cavitation should be consid-
ered in the future study to gain a better insight into the CCPP hydrodynamics. Further develop-
ments will take advantage of the experimental setup and control software designed from this
research study to analyse the cavitation phenomenon in the CCPP.
As mentioned in the previous sections, the CCPP system has its own drawback on the mechan-
ical design. In the scope of this study, the modification of its internal mechanism has not been
considered. The disadvantage is its electro-mechanical complexity in that many linkages are re-
quired to transfer the forces from rotating shaft to the propeller blades. Moreover, the movement
of these components is not as fast as expected. These facts mean that the CCPP would have
lower operational and propulsive efficiency compared to the conventional FPP propulsion in
their current design. It is recommended that the number of actuators could be reduced to two
and their movement direction should be changed so that their generated forces exerting directly
on the swashplate. The modification into a simpler mechanical model would help the system
achieve higher efficiency and faster response in manoeuvring performance.
Constraints of time and budget means the second version of the CCPP prototype has not been
constructed with reference to existing design. For this reason, it was decided that the experi-
mental procedure and simulation framework should be developed in detail for the further re-
search. The next research stage in this project would be able to reuse the current foundation to
design a more efficient propulsion system. The obtained results from this study would be ap-
plied for the optimisation to create a smaller and simpler CCPP propulsion that physically fits
Chapter 8. Conclusions and Future Work
162
into the Gavia AUV platform. The free-running model would definitely give the green light to
the exact evaluation of the proposed system. The results of the free-running trails could be used
to validate the simulation results in this study.
The linear controller is used as the primary control algorithm due to its easy of application in
the development stage. However, application of this controller on the physical prototype system
would not be without difficulty. The analysis of limitations of such controller should be carried
out to determine the boundaries beyond which the CCPP can no longer be under control. An
observer and a navigation system should also be developed and integrated into the control sys-
tem. Moreover, in an attempt to increase the robustness and accuracy of the optimal controller,
the dynamic model of Gavia AUV could be refined in term of the linear and nonlinear hydro-
dynamic coefficients. A better estimation of these parameters using could provide a more accu-
rate controller performance. In addition, different types of control algorithm could also be ex-
amined based on the same platform to verify the obtained results.
Chapter 8. Conclusions and Future Work
163
The innovative Collective and Cyclic Pitch Propeller offers a promising alternative to the traditional
propulsion system. Its superior capability in term of manoeuvrability is validated by various experi-
ments and simulations in this research project. A great deal of effort has been made during the develop-
ment process by scientists and engineers in order to ensure that the innovative CCPP propulsion could
be applied to the new generation of marine underwater vehicles.
Research Team at the Australian Maritime College, University of Tasmania
Launceston, Tasmania, Australia 2017
164
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Appendix A
The experimental procedure for the experiment with CCPP system in chapter 5
Bollard Pull Procedure
Make sure two power generator is on. (10V generator for actuators and 48V generator for
BLDC motor).
Insert the run number in the data sheet and identify experiment condition for the run.
Zero value (initial state) for the external and internal load cell is recorded before the exper-
iment is conducted.
Start the LabVIEW control program:
Blade Control Program:
Enable all actuators and set them in auto mode.
Set the desired value for collective and cyclic angle in percentage.
Wait till the “In tol light” flashed for all actuators.
Shaft speed control program:
Enable the motor amplifier.
Set the control program in auto mode.
Set the desired rpm in conjunction with the experiment condition.
Wait until the rotation speed of the shaft stables.
Start record the data simultaneously for internal and external load cells for 20 seconds.
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Once the data recorded, the rotation of propeller shaft is stopped and the LabVIEW con-
trol program is halted.
Making sure the recorded file is in the correct name.
Captive Test Procedure
Recognized the experiment condition for the run from the data sheet.
The carriage speed is set at the desired value and the direction of the carriage is set in for-
ward state.
Zero value (initial state) for the external and internal load cell is recorded before the exper-
iment is conducted.
Start the LabVIEW control program:
Blade control program:
Enable all actuators and set them in auto mode.
Set the desired value for collective and cyclic angle in percentage.
Wait till the “In tol light” flashed for all actuators.
Shaft speed control program:
Enable the motor amplifier.
Set the control program in auto mode.
Set the desired rpm in conjunction with the experiment condition.
Wait until the rotation speed of the shaft stables.
The carriage power supply is started up and initiated the towing carriage at the desired
speed.
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The data is recorded once the carriage speed reached the desired speed and both external
and internal load cells is recorded simultaneously.
The data is recorded for 20 seconds and the carriage is stopped.
The carriage is moved back to its initial state and the next run is waited for at least 5
minutes due to the wave disturbance after being towed.
Equipment Calibration Photos
Figure A.1. Internal Balance Calibration Setup.
180
Figure A.2. External Balance Calibration Setup.
181
Appendix B
Simulink/Matlab Diagram
Figure B.1. Simulink Model for the Simulation.
Figure B.2. Simulink Model for the Depth Control.
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Figure B.3. Simulink Model for the Heading Control.
Hydrodynamic Coefficients for Gavia standard configuration used in Matlab code
% Geometric Configuration % Note to modify as changing the module attached % L = 2.3 Length (m) % D = 0.2 Maximum Diameter (m) % g= 9.81; %Acceleration due to gravity (kg/m^2) % m= 63; %Total Mass (kg) % W= m*g; %Total weight (N) % B= (m+0.5)*g; %Vehicle Buoyancy % rho= 1000; %Water density % % %Moments of Inertia WRT origin at hafl-length % I_xx= 1; %kg*m^2 % I_yy= 28.5; %kg*m^2 % I_zz= I_yy; %kg*m^2 % I_yz= 0; % I_zy=I_yz;
% Added mass Coefficients and Nonlinear Damping Coefficients for the
hull % % Note that the Added Mass Coefficients have negative values re-
garding to the specified equation of motion in this study.
% X_udot= -6.3; %Added mass (kg) % X_uu= -3.13; %Cross-flow drag (kg/m) % X_wq= -77.8 ; %Added mass cross term (kg/rad) % X_qq= -4.16 ; %Added mass cross term (kg*m/rad) % X_vr= 72 ; %Added mass cross term (kg/rad) % X_rr= -4.16 ; %Added mass cross term (kg*m/rad) % % Y_vdot= -X_vr; %Added mass (kg) % Y_rdot=-X_rr; % Y_vv= -123.9; %Cross-flow drag (kg/m) % Y_rr= -13; %Cross flow drag (kg*m/rad^2) % Y_ur=X_udot; %Added mass cross term and fin lift (kg/rad)
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% Y_wp=-X_wq; %Added mass cross term % Y_pq=-X_qq; %Added mass cross term % Y_uv= 11.6; %Reconsider Consider this! Body lift force
and fin lift % % Z_wdot= X_wq; %Added mass (kg) % Z_qdot= X_qq; %Added mass (kg*m/rad) % Z_ww= -285; %Cross-flow drag (kg/m) % Z_q= -Y_rr; %Cross-flow drag (kg*m/rad) % Z_uq= - 0.884; %Added mass cross term and fin lift (kg/rad) % Z_vp= Y_vdot; %Added mass cross term (kg/rad) % Z_rp= Y_rdot; %Added mass cross term (kg/rad) % Z_uw= Y_uv; %Body lift force and Fin lift (kg/m) % Zuu_gamma_s = -2.13 (kgm/rad) %Fin Lift Force Coefficient (Stern
Plane) % % K_pdot= -0.0104; %Added mass (kg*m^2/rad) % K_pp= -0.13; %Rolling resistance % % M_wdot= Z_qdot; %Added mass (kg*m) % M_qdot= -45.2; %Added mass (kg*m^2/rad) % M_ww= -8.82; %Cross-flow drag (kg) % M_qq= -2810; %Cross-flow drag (kg*m^2/rad^2) % M_uw= -0.548; %Body and Fin Lift and Munk Moment (kg) % M_uq= -X_qq; %Added mass cross-term and fin lift
(kg*m/rad) % M_vp= -M_uq; %Added mass cross-term (kg*m/rad) % M_rp= 45.2; %Added mass cross-term (kg*m^2/rad^2) % Muu_gamma_r = -14.6 (kg/rad) %Fin Lift Moment (Rudder)
% N_vdot= Y_rdot; %Added mass (kg*m) % N_rdot= M_qdot; % N_vv= -M_ww; %Cross-flow drag (kg) % N_rr= M_qq; %Cross-flow drag (kg*m^2/rad^2) % N_ur= M_uq; %Added mass cross-term and fin lift
(kg*m/rad) % N_uv= - 0.548; %Body and Fin lift and Munk moment (kg) % N_wp= -N_ur; %Added mass cross-term (kg*m/rad) % N_pq= -M_rp; %Added mass cross-term (kg*m^2/rad^2) % Nuu_gamma_s = -14.6 (kg/rad) %Fin Lift Moment (Stern-Plane)